@Article{AACI, Title = {Recycling of strange sets: {I. Cycle} expansions}, Author = {Artuso, R. and Aurell, E. and Cvitanovi{\'c}, P.}, Journal = {Nonlinearity}, Year = {1990}, Pages = {325--359}, Volume = {3}, DOI = {10.1088/0951-7715/3/2/005} } @Article{AACII, Title = {Recycling of strange sets: {II. Applications}}, Author = {Artuso, R. and Aurell, E. and Cvitanovi{\'c}, P.}, Journal = {Nonlinearity}, Year = {1990}, Pages = {361--386}, Volume = {3}, DOI = {10.1088/0951-7715/3/2/006} } @Book{Abbas16, title = {{Group Theory in Particle, Nuclear, and Hadron Physics}}, publisher = {CRC Press}, year = {2016}, author = {Abbas, S. A.}, address = {Boca Raton, FL}, doi = {10.1201/9781315371702}, } @Article{AbBrKe91, author = {Abarbanel, H. D. I. and Brown, R. and Kennel, M. B.}, title = {{Lyapunov} exponents in chaotic systems: their importance and their evaluation using observed data}, journal = {Int. J. Mod. Phys. B}, year = {1991}, volume = {5}, pages = {1347--1375}, doi = {10.1142/s021797929100064x}, } @Article{AbBrKe91a, author = {Abarbanel, H. D. I. and Brown, R. and Kennel, M. B.}, title = {Variation of {Lyapunov} exponents on a strange attractor}, journal = {J. Nonlin. Sci.}, year = {1991}, volume = {1}, pages = {175--199}, doi = {10.1007/bf01209065}, } @Article{Abdusalam, Title = {Renormalization group method and {Julia} sets}, Author = {A. Abdusalam}, Journal = {Chaos Solit. Fract.}, Year = {2001}, Pages = {423--428}, Volume = {12}, DOI = {10.1016/S0960-0779(00)00008-4} } @Article{ABLM98, Title = {Is the geometry of nature fractal?}, Author = {Avnir, D. and Biham, O. and Lidar, D. and Malcai, O.}, Journal = {Science}, Year = {1998}, Pages = {39--40}, Volume = {279}, DOI = {10.1126/science.279.5347.39} } @Book{ablowbook, author = {M. J. Ablowitz and P. A. Clarkson}, publisher = {Cambridge Univ. Press}, title = {{Solitions, Nonlinear Evolution Equations and Inverse Scattering}}, year = {1992}, address = {Cambridge UK}, doi = {10.1017/cbo9780511623998}, } @Article{Abraham95, author = {N. B. Abraham and U. A. Allen and E. Peterson and A. Vicens and R. Vilaseca and V. Espinosa and G. L. Lippi}, journal = {Opt. Commun.}, title = {Structural similarities and differences among attractors and their intensity maps in the laser-{Lorenz} model}, year = {1995}, pages = {367--384}, volume = {117}, doi = {10.1016/0030-4018(95)00087-o}, } @Book{AbrMars78, title = {{Foundations of Mechanics}}, publisher = {Benjamin-Cummings}, year = {1978}, author = {R. Abraham and J. E. Marsden}, isbn = {9780821869505}, address = {Reading, MA}, doi = {10.1090/chel/364}, } @Book{AbrSte64, author = {Abramowitz, M. and Stegun, I. A.}, publisher = {Dover}, title = {{Handbook of Mathematical Functions}}, year = {1965}, address = {New York}, edition = {3}, doi = {10.2307/3614753}, } @Book{AbSh92, title = {{Dynamics - The Geometry of Behavior}}, publisher = {Wesley}, year = {1992}, author = {R. H. Abraham and C. D. Shaw}, isbn = {978-0201567175}, address = {Reading, MA}, } @Article{ACFK09, author = {Abarbanel, H. D. I. and Creveling, D. R. and Farsian, R. and Kostuk, M.}, title = {Dynamical state and parameter estimation}, journal = {SIAM J. Appl. Math.}, year = {2009}, volume = {8}, pages = {1341--1381}, doi = {10.1137/090749761}, } @Article{ACHKW11, Title = {Revealing the state space of turbulent pipe flow by symmetry reduction}, Author = {Willis, A. P. and Cvitanovi{\'c}, P. and Avila, M.}, Journal = {J. Fluid Mech.}, Year = {2013}, Pages = {514--540}, Volume = {721}, DOI = {10.1017/jfm.2013.75} } @Article{ACL93, Title = {Periodic orbit theory of anomalous diffusion}, Author = {R. Artuso and G. Casati and R. Lombardi}, Journal = {Phys. Rev. Lett.}, Year = {1993}, Pages = {62}, Volume = {71}, DOI = {10.1103/PhysRevLett.71.62} } @Article{ACL94, Title = {Periodic orbit theory of deterministic diffusion}, Author = {R. Artuso and G. Casati and R. Lombardi}, Journal = {Physica A}, Year = {1994}, Pages = {412--419}, Volume = {205}, DOI = {10.1016/0378-4371(94)90520-7} } @Book{Addison97, title = {{Fractals and Chaos: An illustrated Course}}, publisher = {CRC Press}, year = {1997}, author = {Addison, P. S.}, address = {Boca Raton FL}, isbn = {9780750304009}, doi = {10.1201/9780849384431}, } @Article{AdKoMc65, author = {R. C. Adler and A. C. Konheim and M. H. McAndrew}, title = {Topological entropy}, journal = {Trans. Amer. Math. Soc.}, year = {1965}, volume = {114}, pages = {309--319}, doi = {10.2307/1994177}, } @Article{Adler1977, Title = {Regularization of the stress-energy tensor for vector and scalar particles propagating in a general background metric}, Author = {S. L. Adler and J. Lieberman and Y. J. Ng}, Journal = {Ann. Phys.}, Year = {1977}, Pages = {279--321}, Volume = {106}, DOI = {10.1016/0003-4916(77)90313-X} } @Book{Adler95, title = {{Quaternionic Quantum Mechanics and Quantum Fields}}, publisher = {Oxford Univ. Press}, year = {1995}, author = {S. L. Adler}, isbn = {9780195345063}, doi = {10.1063/1.2807659}, } @Article{ADSK14, author = {Avila, A. and De Simoi, J. and Kaloshin, V.}, title = {An integrable deformation of an ellipse of small eccentricity is an ellipse}, journal = {Ann. Math.}, year = {2016}, volume = {184}, pages = {527--558}, doi = {10.4007/annals.2016.184.2.5}, } @Article{AdWei67, Title = {Entropy, a complete metric invariant for automorphisms of the torus}, Author = {Adler, R. L. and Weiss, B.}, Journal = {Proc. Natl. Acad. Sci. USA}, Year = {1967}, Pages = {1573--1576}, Volume = {57}, DOI = {10.1073/pnas.57.6.1573} } @Article{afind, Title = {Characterization of unstable periodic orbits in chaotic attractors and repellers}, Author = {O. Biham and W. Wenzel}, Journal = {Phys. Rev. Lett.}, Year = {1989}, Pages = {819--822}, Volume = {63}, DOI = {10.1103/PhysRevLett.63.819} } @Article{Afraimovich87, author = {V. S. Afraimovich and B. B. Bykov and L. P. Shilnikov}, title = {On the origin and structure of the {Lorenz} attractor}, journal = {Dokl. Akad. Nauk SSSR}, year = {1977}, volume = {234}, pages = {336--339}, note = {In Russian}, } @Article{AG93, Title = {Fast dynamos and determinants of singular integral operators}, Author = {Aurell, E. and Gilbert, A. D.}, Journal = {Geophys. Astrophys. Fluid Dynam.}, Year = {1993}, Pages = {5--32}, Volume = {73}, DOI = {10.1080/03091929308203617} } @Article{AGHks89, Title = {{Kuramoto-Sivashinsky} dynamics on the center-unstable manifold}, Author = {D. Armbruster and J. Guckenheimer and P. Holmes}, Journal = {SIAM J. Appl. Math.}, Year = {1989}, Pages = {676--691}, Volume = {49}, DOI = {10.1137/0149039} } @Article{AGHO288, Title = {Heteroclinic cycles and modulated travelling waves in systems with {O}(2) symmetry}, Author = {D. Armbruster and J. Guckenheimer and P. Holmes}, Journal = {Physica D}, Year = {1988}, Pages = {257--282}, Volume = {29}, DOI = {10.1016/0167-2789(88)90032-2} } @Article{AGIP90, Title = {On the topology of the {H{\'e}non} map}, Author = {G. D'Alessandro and P. Grassberger and S. Isola and A. Politi}, Journal = {J. Phys. A}, Year = {1990}, Pages = {5285--5294}, Volume = {23}, DOI = {10.1088/0305-4470/23/22/017} } @Article{AGRS86, author = {Aranson, I. S. and {Gaponov-Grekhov}, A. V. and {Rabinovich}, M. I. and {Starobinets}, I. M.}, title = {Strange attractors and the spatial development of turbulence in flow systems}, journal = {Sov. Phys. JETP}, year = {1986}, volume = {63}, pages = {1000}, url = {http://jetp.ac.ru/cgi-bin/dn/e_063_05_1000.pdf} } @Article{Aguir08, Title = {Robust chaos with variable {Lyapunov} exponent in smooth one-dimensional maps}, Author = {Aguirregabiria, J. M.}, Journal = {Chaos Solit. Fract.}, Year = {2009}, Pages = {2531--2539}, Volume = {42}, DOI = {10.1016/j.chaos.2009.03.196} } @Article{ahuja_template-based_2007, Title = {Template-based stabilization of relative equilibria in systems with continuous symmetry}, Author = {S. Ahuja and I. G. Kevrekidis and C. W. Rowley}, Journal = {J. Nonlin. Sci.}, Year = {2007}, Pages = {109--143}, Volume = {17}, DOI = {10.1007/s00332-005-0801-7} } @Article{Airy1838, Title = {On the intensity of light in the neighbourhood of a caustic}, Author = {G. B. Airy}, Journal = {Trans. Camb. Phil. Soc.}, Year = {1838}, Pages = {379--403}, Volume = {6}, URL = {https://archive.org/stream/transactionsofca06camb#page/n401/mode/2up} } @Book{Aitken39, author = {Aitken, A. C.}, publisher = {Oliver \&\ Boyd}, title = {{Determinants \&\ Matrices}}, year = {1939}, address = {Edinburgh}, isbn = {9781473347106}, } @Article{Aizawa84, Title = {Symbolic dynamics approach to the two-{D} chaos in area-preserving maps}, Author = {Aizawa, Y.}, Journal = {Progr. Theor. Phys.}, Year = {1984}, Pages = {1419--1421}, Volume = {71}, DOI = {10.1143/PTP.71.1419} } @Article{AKcgl02, Title = {The world of the complex {Ginzburg-Landau} equation}, Author = {I. S. Aranson and L. Kramer}, Journal = {Rev. Mod. Phys.}, Year = {2002}, Pages = {99--143}, Volume = {74}, DOI = {10.1103/RevModPhys.74.99} } @Article{AlbChe98, author = {A. Albouy and A. Chenciner}, journal = {Inv. Math.}, title = {Le probl{\`e}me des {$N$} corps et les distances mutuelles}, year = {1998}, pages = {151--184}, volume = {31}, doi = {10.1007/0-387-21791-6_9}, } @Article{AleYak81, Title = {Symbolic dynamics and hyperbolic dynamic systems}, Author = {V. M. Alekseev and M. V. Yakobson}, Journal = {Phys. Rep.}, Year = {1981}, Pages = {290--325}, Volume = {75}, DOI = {10.1016/0370-1573(81)90186-1} } @Article{AlIsPo91, Title = {Geometric properties of the pruning front}, Author = {G. D'Alessandro and S. Isola and A. Politi}, Journal = {Progr. Theor. Phys.}, Year = {1991}, Pages = {1149--1157}, Volume = {86}, DOI = {10.1143/ptp/86.6.1149} } @Article{Allah08, author = {Allahverdyan, A. E.}, title = {Entropy of hidden {Markov} processes via cycle expansion}, journal = {J. Stat. Phys.}, year = {2008}, volume = {133}, pages = {535--564}, doi = {10.1007/s10955-008-9613-0}, } @Article{AllgGeorg88, Title = {Numerically stable homotopy methods without an extra dimension}, Author = {E. L. Allgower and K. Georg}, Journal = {Lect. Appl. Math.}, Year = {1990}, Pages = {1--13}, Volume = {26}, URL = {http://www.math.colostate.edu/emeriti/georg/homExtra.pdf} } @Book{AllGeo03, author = {Allgower, E. L. and Georg, K.}, publisher = {SIAM}, title = {{Introduction to Numerical Continuation Methods}}, year = {2003}, city = {Philadelphia}, doi = {10.1137/1.9780898719154}, } @Book{AlLlMi00, author = {Alsed{\`a}, L. and Llibre, J. and Misiurewicz, M.}, publisher = {World Scientific}, title = {{Combinatorial Dynamics and Entropy in Dimension One}}, year = {2000}, address = {Singapore}, doi = {10.1142/4205}, } @Book{almeida88, author = {Ozorio de Almeida, A. M.}, publisher = {Cambridge Univ. Press}, title = {{Hamiltonian Systems: Chaos and Quantization}}, year = {1989}, address = {Cambridge UK}, doi = {10.1017/cbo9780511564161}, } @Article{AltTel08, Title = {Poincar{\'e} recurrences and transient chaos in systems with leaks}, Author = {E. G. Altmann and T. T\'el}, Journal = {Phys. Rev. E}, Year = {2009}, Pages = {016204}, Volume = {79}, DOI = {10.1103/PhysRevE.79.016204} } @Article{alvarez_monodromy_2005, author = {M. {\'A}lvarez and A. Gasull}, journal = {Int. J. Bifur. Chaos}, title = {Monodromy and stability for nilpotent critical points}, year = {2005}, pages = {1253--1265}, volume = {15}, doi = {10.1142/S0218127405012740}, } @Book{Ambeg96, author = {Ambegaokar, V.}, publisher = {Cambridge Univ. Press}, title = {{Reasoning about Luck: Probability and Its Uses in Physics}}, year = {1996}, address = {Cambridge UK}, doi = {10.1017/cbo9781139170581}, } @Article{AMGN, author = {Alonso, D. and D. MacKernan, P. Gaspard and Nicolis, G.}, journal = {Phys. Rev. E}, title = {Statistical approach to nonhyperbolic chaotic systems}, year = {1996}, pages = {2474}, volume = {54}, doi = {10.1103/PhysRevE.54.2474}, } @InCollection{ampatt, author = {van Hecke, M. and Hohenberg, P. C. and van Saarloos, W.}, booktitle = {{Fundamental Problems in Statistical Mechanics}}, publisher = {North-Holland}, title = {Amplitude equations for pattern forming systems}, year = {1994}, address = {Amsterdam}, editor = {van Beijeren, H. and Ernst, M. H.}, volume = {VIII}, doi = {10.1016/b978-0-444-81591-0.50014-6}, } @Article{AmZaSa10, Title = {Permutation complexity of spatiotemporal dynamics}, Author = {J. M. Amig{\'o} and S. Zambrano and M. A. F. Sanju{\'a}n}, Journal = {Europhys. Lett.}, Year = {2010}, Pages = {10007}, Volume = {90}, DOI = {10.1209/0295-5075/90/10007} } @Book{AnAr88, Title = {{Dynamical systems {I}: {Ordinary} Differential Equations and Smooth Dynamical Systems}}, Author = {D. V. Anosov and V. I. Arnol'd}, Publisher = {Springer}, Year = {1988}, Address = {New York}, ISBN = {978-3-540-17000-6} } @Article{AnBoAi07, author = {Ando, H. and Boccaletti, S. and Aihara, K.}, title = {Automatic control and tracking of periodic orbits in chaotic systems}, journal = {Phys. Rev. E}, year = {2007}, volume = {75}, pages = {066211}, doi = {10.1103/physreve.75.066211}, } @Article{AndCom07, Title = {Relativistic fluid dynamics: {Physics} for many different scales}, Author = {N. Andersson and G. L. Comer}, Journal = {Living Reviews in Relativity}, Year = {2007}, Pages = {1--83}, Volume = {10}, DOI = {10.12942/lrr-2007-1} } @Article{AnDiMa08, author = {Antoneli, F. and Dias, A. P. S. and Matthews, P. C.}, title = {Invariants, equivariants and characters in symmetric bifurcation theory}, journal = {Proc. R. Soc. Edinburgh A}, year = {2008}, volume = {138}, pages = {477--512}, doi = {10.1017/S0308210506001119}, } @Article{angen88, author = {S. B. Angenent}, title = {The periodic orbits of an area preserving twist-map}, journal = {Commun. Math. Phys.}, year = {1988}, volume = {115}, pages = {353--374}, doi = {10.1007/bf01218016}, } @Article{AngMor12, Title = {An approximate formula for the diffusion coefficient for the periodic {Lorentz} gas}, Author = {C. Angstmann and G .P. Morriss}, Journal = {Phys. Lett. A}, Year = {2012}, Pages = {1819--1822}, Volume = {376}, DOI = {10.1016/j.physleta.2012.04.045} } @Article{AnoSin67, author = {Anosov, D. V. and Sinai, Ya. G.}, journal = {Russ. Math. Surv.}, title = {Some smooth ergodic systems}, year = {1967}, pages = {103--167}, volume = {22}, doi = {10.1070/RM1967v022n05ABEH001228}, } @Article{anosov67, author = {D. V. Anosov}, journal = {Proc. Steklov Inst. of Math.}, title = {Geodesic flows on compact {Riemannian} manifolds of negative curvature}, year = {1967}, pages = {1--235}, volume = {90}, url = {http://mi.mathnet.ru/eng/tm2795}, } @Book{AP86, title = {{Inward Bound: of Matter and Forces in the Physical World}}, publisher = {Oxford Univ. Press}, year = {1986}, author = {A. Pais}, address = {Oxford}, doi = {10.1063/1.2815127}, } @Book{AP91, title = {{Niels Bohr's Times, in Physics, Philosophy and Polity}}, publisher = {Oxford Univ. Press}, year = {1991}, author = {A. Pais}, address = {Oxford}, doi = {10.1063/1.2809577}, } @Book{ArKoNe88, title = {{Mathematical Aspects of Classical and Celestial Mechanics}}, publisher = {Springer}, year = {1988}, author = {V. I. Arnol'd and V. V. Kozlov and A. I. Neishtadt}, address = {New York}, doi = {10.1007/978-3-540-48926-9}, } @Book{ArnAve, title = {{Ergodic Problems of Classical Mechanics}}, publisher = {Addison-Wesley}, year = {1989}, author = {V. I. Arnol'd and A. Avez}, address = {Redwood City}, isbn = {9781475720631}, } @Book{arnold89, title = {{Mathematical Methods for Classical Mechanics}}, publisher = {Springer}, year = {1989}, author = {V. I. Arnol'd}, isbn = {9781475720631}, address = {New York}, doi = {10.1007/978-1-4757-2063-1}, } @Article{arnold91k, author = {V. I. Arnol'd}, title = {Kolmogorov's hydrodynamic attractors}, journal = {Proc. R. Soc. Lond. A}, year = {1991}, volume = {434}, pages = {19--22}, doi = {10.1098/rspa.1991.0077}, } @Book{arnold92, title = {{Ordinary Differential Equations}}, publisher = {Springer}, year = {1992}, author = {V. I. Arnol'd}, isbn = {978-3-540-34563-3}, address = {New York}, doi = {10.2307/2324802}, } @Book{ArnoldL74, title = {{Stochastic Differential Equations: Theory and Applications}}, publisher = {Wiley}, year = {1974}, author = {Arnold, L.}, isbn = {9780486482361}, address = {New York}, doi = {10.2307/2344856}, } @Article{art03, Title = {Cycle expansions for intermittent maps}, Author = {R. Artuso and P. Cvitanovi{\'c} and G. Tanner}, Journal = {Proc. Theor. Phys. Supp.}, Year = {2003}, Pages = {1--21}, Volume = {150}, DOI = {10.1143/PTPS.150.1} } @Article{art91, Title = {Diffusive dynamics and periodic orbits of dynamic systems}, Author = {R. Artuso}, Journal = {Phys. Lett. A}, Year = {1991}, Pages = {528--530}, Volume = {160}, DOI = {10.1016/0375-9601(91)91062-I} } @Incollection{ArtBur14, author = {Artuso, R. and Burioni, R.}, title = {Anomalous diffusion: {Deterministic} and stochastic perspectives}, booktitle = {{Large Deviations in Physics: The Legacy of the Law of Large Numbers}}, publisher = {Springer}, year = {2014}, editor = {Vulpiani, A. and Cecconi, F. and Cencini, M. and Puglisi, A. and Vergni, D.}, pages = {263--293}, address = {Berlin}, doi = {10.1007/978-3-642-54251-0_10}, isbn = {978-3-642-54250-3}, } @Article{ArtCri03, Title = {Weak chaos and anomalous transport: a deterministic approach}, Author = {R. Artuso and G. Cristadoro}, Journal = {Commun. Nonlinear Sci. Numer. Simul.}, Year = {2003}, Pages = {137--148}, Volume = {8}, DOI = {10.1016/S1007-5704(03)00025-X} } @Incollection{ArtCri08, author = {Artuso, R. and Cristadoro, G.}, title = {Deterministic (anomalous) transport}, booktitle = {{Anomalous Transport: Foundations and Applications}}, publisher = {Wiley}, year = {2008}, editor = {Klages, R. and Radons, G. and Sokolov, I. M.}, isbn = {9783527407224}, address = {New York}, doi = {10.1002/9783527622979.ch8}, } @Article{ArtStr97, Title = {Reycling diffusion in sawtooth and cat maps}, Author = {R. Artuso and R. Strepparava}, Journal = {Phys. Lett. A}, Year = {1997}, Pages = {469--475}, Volume = {236}, DOI = {10.1016/S0375-9601(97)00792-5} } @Article{Artuso88, author = {R. Artuso}, title = {Logarithmic strange sets}, journal = {J. Phys. A}, year = {1988}, volume = {21}, pages = {L923--L927}, doi = {10.1088/0305-4470/21/19/001}, } @Article{Artuso94, Title = {Recycling deterministic diffusion}, Author = {R. Artuso}, Journal = {Physica D}, Year = {1994}, Pages = {1--7}, Volume = {76}, DOI = {10.1016/0167-2789(94)90245-3} } @Book{ArWe05, author = {G. B. Arfken and H. J. Weber}, publisher = {Academic}, title = {{Mathematical Methods for Physicists: A Comprehensive Guide}}, year = {2005}, address = {New York}, edition = {6}, isbn = {9780123846549}, } @Book{ArWeHa13, author = {G. B. Arfken and H. J. Weber and F. E. Harris}, publisher = {Academic}, title = {{Mathematical Methods for Physicists: A Comprehensive Guide}}, year = {2013}, address = {New York}, edition = {7}, isbn = {9780123846549}, } @Article{AS87, author = {M. S. Acarlar and C. R. Smith}, title = {A study of hairpin vortices in a laminar boundary layer. {Part 1. Hairpin} vortices generated by a hemisphere protuberance}, journal = {J. Fluid Mech.}, year = {1987}, volume = {175}, pages = {1--41}, doi = {10.1017/S0022112087000272}, } @Article{AS87a, author = {M. S. Acarlar and C. R. Smith}, title = {A study of hairpin vortices in a laminar boundary layer. {Part 2. Hairpin} vortices generated by fluid injection}, journal = {J. Fluid Mech.}, year = {1987}, volume = {175}, pages = {45--83}, doi = {10.1017/S0022112087000284}, } @Article{Asa06, Title = {Statistical properties of periodic orbits in a 4-disk billiard system: {The} pruning-proof property}, Author = {Asamizuya, T.}, Journal = {Progr. Theor. Phys.}, Year = {2006}, Pages = {247--271}, Volume = {116}, DOI = {10.1143/PTP.116.247} } @Article{Ascher95, Title = {Implicit-explicit methods for time-dependent partial differential equations}, Author = {U. M. Ascher and S. J. Ruuth and B. T. R. Wetton}, Journal = {SIAM J. Numer. Anal.}, Year = {1995}, Pages = {797--823}, Volume = {32}, DOI = {10.1137/0732037} } @Article{AschKnauf97, Title = {Motion in periodic potentials}, Author = {Asch, J. and Knauf, A.}, Journal = {Nonlinearity}, Year = {1998}, Pages = {175--200}, Volume = {11}, DOI = {10.1088/0951-7715/11/1/011} } @Book{AshMer, title = {{Solid State Physics}}, publisher = {Holt, Rinehart and Winston}, year = {1976}, author = {Ashcroft, N. W. and Mermin, N. D.}, isbn = {0030839939}, doi = {10.1063/1.3037370}, } @Article{AstMelb06, Title = {{Lyapunov} exponents of symmetric attractors}, Author = {P. Aston and I. Melbourne}, Journal = {Nonlinearity}, Year = {2006}, Pages = {2455--2466}, Volume = {19}, DOI = {10.1088/0951-7715/19/10/010} } @Book{ASY96, author = {Alligood, K. T. and Sauer, T. D. and Yorke, J. A.}, publisher = {Springer}, title = {{Chaos, An Introduction to Dynamical Systems}}, year = {1996}, address = {New York}, doi = {10.1007/b97589}, } @Article{AtJaJo10, author = {F. M. Atay and S. Jalan and J. Jost}, journal = {Phys. Lett. A}, title = {Symbolic dynamics and synchronization of coupled map networks with multiple delays}, year = {2010}, pages = {130--135}, volume = {375}, doi = {10.1016/j.physleta.2010.10.044}, } @Article{atlas12, Title = {Cartography of high-dimensional flows: {A} visual guide to sections and slices}, Author = {Cvitanovi{\'c}, P. and Borrero-Echeverry, D. and Carroll, K. and Robbins, B. and Siminos, E.}, Journal = {Chaos}, Year = {2012}, Pages = {047506}, Volume = {22}, DOI = {10.1063/1.4758309} } @Article{aub95ant, author = {S. Aubry}, title = {Anti-integrability in dynamical and variational problems}, journal = {Physica D}, year = {1995}, volume = {86}, pages = {284--296}, doi = {10.1016/0167-2789(95)00109-h}, } @Article{Aubry88, Title = {The dynamics of coherent structures in the wall region of turbulent boundary layer}, Author = {N. Aubry and P. Holmes and J. L. Lumley and E. Stone}, Journal = {J. Fluid Mech.}, Year = {1988}, Pages = {115--173}, Volume = {192}, DOI = {10.1017/S0022112088001818} } @Article{Aurell90, author = {Aurell, E.}, title = {Convergence of dynamical zeta functions}, journal = {J. Stat. Phys.}, year = {1990}, volume = {58}, pages = {967--995}, doi = {10.1007/BF01026559}, } @Book{ausloos_logistic_2005, title = {{The Logistic Map and the Route to Chaos: From the Beginnings to Modern Applications}}, publisher = {Springer}, year = {2005}, author = {M. Ausloos and M. Dirickx}, address = {New York}, } @Article{AusYor80, Title = {Interval maps, factors of maps, and chaos}, Author = {Auslander, J. and Yorke, J. A.}, Journal = {Tohoku Math. J.}, Year = {1980}, Pages = {177--188}, Volume = {32}, DOI = {10.2748/tmj/1178229634} } @InCollection{autod89, author = {A. Griewank}, booktitle = {{Math. Proc. Cambridge Philos. Soc.}}, publisher = {Kluwer}, title = {On automatic differentiation}, year = {1989}, address = {Amsterdam}, editor = {M. Iri and K. Tanabe}, pages = {83--108}, } @Article{ave99, Title = {Average patterns of spatiotemporal chaos: {A} boundary effect}, Author = {V. M. Egu\'{i}luz and P. Alstr{\o}m and E. Hern\'{a}ndez-Garc\'{i}a and O. Piro}, Journal = {Phys. Rev. E}, Year = {1999}, Pages = {2822--2825}, Volume = {59}, DOI = {10.1103/PhysRevE.59.2822} } @InCollection{aver_dasbuch, author = {P. Cvitanovi{\'c}}, title = {Averaging}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2020}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/paper.shtml#average}, } @Article{AxFl09, author = {Axenides, M. and Floratos, E.}, journal = {J. High Energy Phys.}, title = {Strange attractors in dissipative {Nambu} mechanics: {Classical} and quantum aspects}, year = {2010}, pages = {036}, volume = {1004}, doi = {10.1007/JHEP04(2010)036}, } @Article{B84, author = {D. J. Benney}, title = {The evolution of disturbances in shear flows at high {R}eynolds numbers}, journal = {Stud. Appl. Math.}, year = {1984}, volume = {70}, pages = {1--19}, doi = {10.1002/sapm19847011}, } @Article{B95, Title = {Infinite kneading matrices and weighted zeta functions of interval maps}, Author = {V. Baladi}, Journal = {J. Functional Analysis}, Year = {1995}, Pages = {226--244}, Volume = {128}, DOI = {10.1006/jfan.1995.1029} } @Article{BaaRob05, Title = {Symmetries and reversing symmetries of polynomial automorphisms of the plane}, Author = {M. Baake and J. A. G. Roberts}, Journal = {Nonlinearity}, Year = {2004}, Pages = {791--816}, Volume = {18}, DOI = {10.1088/0951-7715/18/2/017} } @Article{BaEvCo93, Title = {Field-dependent conductivity and diffusion in a two-dimensional {Lorentz} gas}, Author = {Baranyai, A. and Evans, D. J. and Cohen, E. G. D.}, Journal = {J. Stat. Phys.}, Year = {1993}, Pages = {1085--1098}, Volume = {70}, DOI = {10.1007/BF01049423} } @Misc{Baez06, Title = {This {Week's Finds in Mathematical Physics Week 236}}, Author = {Baez, J.}, Year = {2006}, URL = {http://sci.tech-archive.net/Archive/sci.physics.research/msg00062.html} } @Article{Bai07, Title = {On the cycle expansion for the {Lyapunov} exponent of a product of random matrices}, Author = {Z.-Q. Bai}, Journal = {J. Phys. A}, Year = {2007}, Pages = {8315}, Volume = {40}, DOI = {10.1088/1751-8113/40/29/008} } @Book{BaJeGu02, Title = {{Digraphs: Theory, Algorithms and Applications}}, Author = {Bang-Jensen, J. and Gutin, G. Z.}, Publisher = {Springer}, Year = {2008}, Address = {London}, ISBN = {9781848009981} } @InBook{BaJePo13, author = {O. F. Bandtlow and O. Jenkinson and M. Pollicott}, chapter = {Periodic points, escape rates and escape measures}, editor = {Bahsoun, W. and Bose, C. and Froyland, G.}, pages = {41--58}, publisher = {Springer}, title = {{Ergodic Theory, Open Dynamics, and Coherent Structures}}, year = {2014}, address = {New York}, isbn = {978-1-4939-0419-8}, doi = {10.1007/978-1-4939-0419-8_3}, } @Article{BakasovAbraham93, author = {Bakasov, A. A. and Abraham, N. B.}, title = {Laser second threshold: {Its} exact analytical dependence on detuning and relaxation rates}, journal = {Phys. Rev. A}, year = {1993}, volume = {48}, pages = {1633--1660}, doi = {10.1103/physreva.48.1633}, } @Article{BaKnTu90, Title = {Spiral wave dynamics in a simple model of excitable media: {Transition} from simple to compound rotation}, Author = {D. Barkley and M. Kness and L. S. Tuckerman}, Journal = {Phys. Rev. A}, Year = {1990}, Pages = {2489--2492}, Volume = {42}, DOI = {10.1103/PhysRevA.42.2489} } @Book{Baladi00, title = {{Positive Transfer Operators and Decay of Correlations}}, publisher = {World Scientific}, year = {2000}, author = {Baladi, V.}, isbn = {978-981-02-3328-0}, address = {Singapore}, doi = {10.1142/9789812813633}, } @Article{Baladi07, Title = {On the susceptibility function of piecewise expanding interval maps}, Author = {Baladi, V.}, Journal = {Commun. Math. Phys.}, Year = {2007}, Pages = {839--859}, Volume = {275}, DOI = {10.1007/s00220-007-0320-5} } @Article{Baladi08, Title = {Linear response despite critical points}, Author = {V. Baladi}, Journal = {Nonlinearity}, Year = {2008}, Pages = {T81--T90}, Volume = {21}, DOI = {10.1088/0951-7715/21/6/T01} } @Misc{Baladi14, author = {V. Baladi}, title = {Linear response, or else}, year = {2014}, eprint = {1408.2937}, eprinttype = {arxiv}, } @Inproceedings{Baladi95, author = {V. Baladi}, title = {Dynamical zeta functions}, booktitle = {{Real and Complex Dynamical Systems: Proceedings of the NATO ASI}}, year = {1995}, editor = {B. Branner and P. Hjorth}, pages = {1--26}, address = {Dordrecht}, publisher = {Kluwer}, doi = {10.1007/978-94-015-8439-5_1}, } @InProceedings{Baladi95a, author = {V. Baladi}, booktitle = {{XIth Intern. Congr. Math.Phys., Paris 1994}}, title = {Dynamical zeta function and generalised {Fredholm} determinants}, year = {1995}, address = {Cambridge UK}, editor = {Iagolnitzer, D.}, pages = {249--260}, publisher = {Cambridge Univ. Press}, isbn = {9781571460301}, url = {http://webusers.imj-prg.fr/~viviane.baladi/icmp94.ps}, } @Article{Baladi98, author = {Baladi, V.}, title = {Periodic orbits and dynamical spectra}, journal = {Ergod. Theor. Dynam. Syst.}, year = {1998}, volume = {18}, pages = {255--292}, doi = {10.1017/s0143385798113925}, } @Article{Baldwin88, Title = {Soft billiard systems}, Author = {Baldwin, P. R.}, Journal = {Physica D}, Year = {1988}, Pages = {321--342}, Volume = {29}, DOI = {10.1016/0167-2789(88)90034-6} } @Article{BalKel90, author = {V. Baladi and G. Keller}, title = {Zeta functions and transfer operators for piecewise monotone transformations}, journal = {Commun. Math. Phys.}, year = {1990}, volume = {127}, pages = {459--477}, doi = {10.1007/BF02104498} } @Article{BalSma08, Title = {Linear response formula for piecewise expanding unimodal maps}, Author = {V. Baladi and D. Smania}, Journal = {Nonlinearity}, Year = {2008}, Pages = {677}, Volume = {21}, DOI = {10.1088/0951-7715/21/4/003} } @Article{BalTod15, author = {Baladi, V. and Todd, M.}, title = {Linear response for intermittent maps}, journal = {Commun. Math. Phys.}, year = {2016}, volume = {347}, pages = {857--874}, doi = {10.1007/s00220-016-2577-z}, } @Article{baranger, Title = {Periodic trajectories for a two-dimensional nonintegrable {Hamiltonian}}, Author = {M. Baranger and K. T. R. Davies}, Journal = {Ann. Phys.}, Year = {1987}, Pages = {330--358}, Volume = {177}, DOI = {10.1016/0003-4916(87)90123-0} } @Article{baranger88, Title = {The calculation of periodic trajectories}, Author = {M. Baranger and K. T. R. Davies and J. H. Mahoney}, Journal = {Ann. Phys.}, Year = {1988}, Pages = {95--110}, Volume = {186}, DOI = {10.1016/S0003-4916(88)80018-6} } @Article{Barbaro07, author = {G. Barbaro}, title = {Formal solutions of the {Cvitanovi{\'c}-Feigenbaum} equation}, journal = {Int. J. Bifur. Chaos}, year = {2007}, volume = {17}, pages = {3275--3280}, doi = {10.1142/s0218127407019020}, } @Article{BarChor98, author = {G. I. Barenblatt and A. J. Chorin}, title = {New perspectives in turbulence: {Scaling} laws, asymptotics, and intermittency}, journal = {SIAM Rev.}, year = {1998}, volume = {40}, pages = {265--291}, doi = {10.1137/s0036144597320047}, } @Article{Barkley94, author = {Barkley, D.}, title = {{Euclid}ean symmetry and the dynamics of rotating spiral waves}, journal = {Phys. Rev. Lett.}, year = {1994}, volume = {72}, pages = {164--167}, doi = {10.1103/PhysRevLett.72.164}, } @Book{barnsley, author = {Barnsley, M. F.}, publisher = {Dover}, title = {{Fractals Everywhere}}, year = {2012}, address = {New York}, isbn = {9780486320342}, } @Article{Bartholdi14, author = {L. Bartholdi}, title = {{Zeta} functions of graphs: a stroll through the garden, by {Audrey Terras}. Book review}, journal = {Bull. Amer. Math. Soc.}, year = {2014}, doi = {10.1090/S0273-0979-2013-01426-5}, isbn = {978-0-521-11367-0} } @Article{BaSpTr94, author = {Balmforth, N. J. and Spiegel, E. A. and Tresser, C.}, title = {Topological entropy of one-dimensional maps: {Approximations} and bounds}, journal = {Phys. Rev. Lett.}, year = {1994}, volume = {72}, pages = {80--83}, doi = {10.1103/PhysRevLett.72.80} } @Article{Bass74, Title = {Stationary functions and their applications to the theory of turbulence: {I. Stationary} functions}, Author = {J. Bass}, Journal = {J. Math. Anal. Appl.}, Year = {1974}, Pages = {354--399}, Volume = {47}, DOI = {10.1016/0022-247X(74)90026-2} } @Incollection{Basu07, author = {A. Basu}, title = {Construction of {Poincar\'e} return maps for {R\"ossler} flow}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Georgia Inst. of Technology}, year = {2007}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Atlanta}, url = {http://ChaosBook.org/projects/index.shtml#Basu}, } @Article{BaTo03, Title = {Correlation decay in certain soft billiards}, Author = {B\'alint, P. and T\'oth, I. P.}, Journal = {Commun. Math. Phys.}, Year = {2003}, Pages = {55--91}, Volume = {243}, DOI = {10.1007/s00220-003-0954-x} } @Article{BaTo04, Title = {Mixing and its rate in `soft' and `hard' billiards motivated by the {Lorentz} process}, Author = {B\'alint, P. and T\'oth, I. P.}, Journal = {Physica D}, Year = {2004}, Pages = {128--135}, Volume = {187}, DOI = {10.1016/j.physd.2003.09.004} } @Article{BaVo86, Title = {Chaos on the pseudosphere}, Author = {N. L. Balasz and A. Voros}, Journal = {Phys. Rep.}, Year = {1986}, Pages = {109--240}, Volume = {143}, DOI = {10.1016/0370-1573(86)90159-6} } @Article{BBBBF09, Title = {Computation of the response functions of spiral waves in active media}, Author = {I. V. Biktasheva and D. Barkley and V. N. Biktashev and G. V. Bordyugov and A. J. Foulkes}, Journal = {Phys. Rev. E}, Year = {2009}, Pages = {056702}, Volume = {79}, DOI = {10.1103/PhysRevE.79.056702} } @Article{BBJ85, Title = {Mode-locking and the transition to chaos in dissipative systems}, Author = {P. Bak and T. Bohr and M. H. Jensen}, Journal = {Physica Scripta}, Year = {1985}, Pages = {50--58}, Volume = {T9}, DOI = {10.1088/0031-8949/1985/T9/007} } @Article{BBLM93, Title = {Quantum beats and chaos in the {H{\'e}non-Heiles Hamiltonian}}, Author = {M. Brack and R. K. Bhaduri, J. Law and M. V. N. Murthy}, Journal = {Phys. Rev. Lett.}, Year = {1993}, Pages = {568--571}, Volume = {70}, DOI = {10.1103/PhysRevLett.70.568} } @Inproceedings{BC89, author = {M. Benedicks and L. Carleson}, title = {On the {H{\'e}non} attractor}, booktitle = {{IXth Int. Congr. on Mathematical Physics}}, year = {1989}, editor = {B. Simon and A. Truman and M. Davies}, isbn = {9780852742501}, pages = {498--500}, address = {Bristol UK}, publisher = {Adam Hilger}, } @Article{BCFH62, Title = {{D\"unnste Kohlenstoff-Folien}}, Author = {H. P. Boehm. and A. Clauss and G. O. Fischer and U. Hofmann}, Journal = {Z. Naturf. B}, Year = {1962}, Pages = {150--153}, Volume = {17}, DOI = {10.1515/znb-1962-0302} } @Article{BCFLR08, Title = {Abundance of regular orbits and out-of-equilibrium phase transitions in the thermodynamic limit for long-range systems}, Author = {R. Bachelard and C. Chandre and D. Fanelli and X. Leoncini and S. Ruffo}, Journal = {Phys. Rev. Lett.}, Year = {2008}, Pages = {260603}, Volume = {101}, DOI = {10.1103/PhysRevLett.101.260603} } @Article{BCISV93, Title = {Advection of vector fields by chaotic flows}, Author = {Balmforth, N. J. and Cvitanovi{\'c}, P. and Ierley, G. R. and Spiegel, E. A. and Vattay, G.}, Journal = {Ann. New York Acad. Sci.}, Year = {1993}, Pages = {148--160}, Volume = {706}, DOI = {10.1111/j.1749-6632.1993.tb24687.x} } @Article{BCOR11, author = {Botella-Soler, V. and Castelo, J. M. and Oteo, J. A. and Ros, J.}, title = {Bifurcations in the {Lozi} map}, journal = {J. Phys. A}, year = {2011}, volume = {44}, pages = {305101}, doi = {10.1088/1751-8113/44/30/305101}, } @Article{BD97, Title = {Symbolic dynamics and periodic orbits for the cardioid billiard}, Author = {A. B\"acker and H. R. Dullin}, Journal = {J. Phys. A.}, Year = {1997}, Pages = {1991--2020}, Volume = {30}, DOI = {10.1088/0305-4470/30/6/023} } @Article{BDS98, author = {Briggs, K. M. and Dixon, T. W. and Szekeres, G.}, title = {Analytic solutions of the {Cvitanovi{\'c}-Feigenbaum} and {Feigenbaum-Kadanoff-Shenker} equations}, journal = {Int. J. Bifur. Chaos}, year = {1998}, volume = {8}, pages = {347--357}, doi = {10.1142/S0218127498000206}, } @Article{Beck, Title = {Physical meaning for {Mandelbrot} and {Julia} sets}, Author = {C. Beck}, Journal = {Physica D}, Year = {1999}, Pages = {171--182}, Volume = {125}, DOI = {10.1016/S0167-2789(98)00243-7} } @Article{Beem2016, author = {Beem, C. and Lemos, M.a and Liendo, P. and Rastelli, L. and Rees, B. C.}, journal = {J. High Energy Phys.}, title = {The {N = 2} superconformal bootstrap}, year = {2016}, pages = {1--101}, volume = {2016}, doi = {10.1007/JHEP03(2016)183}, } @Book{BeGe06, title = {{Noise-Induced Phenomena in Slow-Fast Dynamical Systems: A Sample-Paths Approach}}, publisher = {Springer}, year = {2005}, author = {Berglund, N. and Gentz, B.}, address = {Berlin}, isbn = {9781846281860}, } @Article{Bel58, author = {L. Bel}, title = {{\'E}tude alg\'ebrique d'un certain type de tenseurs de courbure. {Le} cas 3 de {Petrov}}, journal = {C. R. Acad. Sci., Paris}, year = {1958}, volume = {247}, pages = {2096--2099}, url = {http://gallica.bnf.fr/ark:/12148/bpt6k7258/f1138.item.r=certain%20type%20de%20tenseurs%20de%20courbure.zoom}, } @Article{belit78, author = {R. Belitskii}, title = {Equivalence and normal forms of germs of smooth mappings}, journal = {Russ. Math. Surv.}, year = {1978}, volume = {31}, pages = {107}, doi = {10.1070/rm1978v033n01abeh002237}, } @Book{Bell57, Title = {{Dynamic Programming}}, Author = {Bellman, R.}, Publisher = {Princeton Univ. Press}, Year = {1957}, Address = {Princeton}, ISBN = {9780486317199} } @Book{Bell60, author = {Bellman, R.}, publisher = {SIAM}, title = {{Introduction to Matrix Analysis}}, year = {1997}, address = {Philadelphia}, edition = {2}, isbn = {9781611971170}, } @Article{BenCar85, author = {M. Benedicks and L. Carleson}, journal = {Ann. Math.}, title = {On iterations of {$1 - ax^2$ on $(- 1,1)$}}, year = {1985}, pages = {1--25}, volume = {122}, doi = {10.2307/1971367}, } @Article{BenCar91, Title = {The dynamics of the {H{\'e}non} map}, Author = {M. Benedicks and L. Carleson}, Journal = {Ann. Math.}, Year = {1991}, Pages = {73}, Volume = {133}, DOI = {10.2307/2944326} } @Article{BenCho89, author = {D. J. Benney and K. A. Chow}, title = {A mean flow first harmonic theory for hydrodynamic instabilities}, journal = {Stud. Appl. Math.}, year = {1989}, volume = {80}, pages = {37--73}, doi = {10.1002/sapm198980137}, } @Article{bene80a, author = {Benettin, G. and Galgani, L. and Giorgilli, A. and Strelcyn, J. M.}, journal = {Meccanica}, title = {{Lyapunov} characteristic exponents for smooth dynamical systems; a method for computing all of them. {Part 1: Theory}}, year = {1980}, pages = {9--20}, volume = {15}, doi = {10.1007/BF02128236}, } @Article{bene80b, author = {Benettin, G. and Galgani, L. and Giogilli, A. and Strelcyn, J. M.}, journal = {Meccanica}, title = {{Lyapunov} characteristic exponents for smooth dynamical systems; a method for computing all of them. {Part 2: Numerical} application}, year = {1980}, pages = {21--30}, volume = {15}, doi = {10.1007/BF02128237}, } @Article{BenKS66, author = {Benney, D. J.}, title = {Long waves on liquid films}, journal = {J. Math. Phys}, year = {1966}, volume = {45}, pages = {150}, doi = {10.1002/sapm1966451150}, } @Book{BenOrs78, title = {{Advanced Mathematical Methods for Scientists and Engineers}}, publisher = {McGrow-Hill}, year = {1978}, author = {C. M. Bender and S. A. Orszag}, isbn = {9780387989310}, address = {New York}, doi = {10.1007/978-1-4757-3069-2}, } @Article{BenYou92, Title = {Absolutely continuous invariant measures and random perturbations for certain one-dimensional map}, Author = {M. Benedicks and L.-S. Young}, Journal = {Ergod. Theor. Dynam. Syst.}, Year = {1992}, Pages = {13--37}, Volume = {12}, DOI = {10.1017/S0143385700006556} } @Incollection{BeOtRo14, author = {Beyn, W.-J. and Otten, D. and Rottmann-Matthes, J.}, title = {Stability and computation of dynamic patterns in {PDEs}}, booktitle = {{Current Challenges in Stability Issues for Numerical Differential Equations}}, publisher = {Springer}, year = {2014}, series = {Lect. Notes Math.}, pages = {89--172}, doi = {10.1007/978-3-319-01300-8_3}, editors = {Dieci, L. and Guglielmi, N.}, } @Misc{JePoVy20, author = {Jenkinson, O. and Pollicott, M. and Vytnova, P.}, title = {How many inflections are there in the {Lyapunov} spectrum?}, year = {2020}, eprint = {2002.07781}, eprinttype = {arxiv}, } @Article{BER89, Title = {Resonances for intermittent systems}, Author = {V. Baladi and J.-P. Eckmann and D. Ruelle}, Journal = {Nonlinearity}, Year = {1989}, Pages = {119--135}, Volume = {2}, URL = {http://stacks.iop.org/0951-7715/2/i=1/a=007} } @Article{BergBriggs, Title = {Nonlinear dynamics of intermittent-contact mode atomic force microscopy}, Author = {J. Berg and G. A. D. Briggs}, Journal = {Phys. Rev. B}, Year = {1997}, Pages = {14899}, Volume = {55}, DOI = {10.1103/PhysRevB.55.14899} } @Article{Berkooz94, author = {G. Berkooz and P. Holmes and J. L. Lumley and N. Aubry and E. Stone}, title = {Observations regarding ``{Coherence} and chaos in a model of turbulent boundary layer'' by {X}. {Z}hou and {L}. {S}irovich}, journal = {Phys. Fluids}, year = {1994}, volume = {6}, pages = {1574--1578}, doi = {10.1063/1.868270}, } @Article{Berry02, author = {M. V. Berry}, journal = {Phil. Trans. Roy. Soc. A}, title = {Exuberant interference: {Rainbows}, tides, edges, (de)coherence}, year = {2002}, pages = {1023--1037}, volume = {360}, doi = {10.1098/rsta.2001.0979}, url = {http://www.phy.bris.ac.uk/people/berry_mv/the_papers/Berry342.pdf}, } @Article{Berry12, author = {M. V. Berry}, journal = {Commun. Swiss Phys. Soc.}, title = {{Martin Gutzwiller} and his periodic orbits}, year = {2012}, pages = {34--38}, volume = {37}, url = {http://www.sps.ch/fileadmin/_migrated/content_uploads/Mitteilungen.37.pdf}, } @Article{Berry84, Title = {Quantal phase factors accompanying adiabatic changes}, Author = {Berry, M. V.}, Journal = {Proc. R. Soc. Lond. A}, Year = {1984}, Pages = {45--57}, Volume = {392}, DOI = {10.1098/rspa.1984.0023} } @InBook{Berry86, author = {Berry, M. V.}, editor = {Seligman, T. H. and Nishioka, H.}, pages = {1--17}, publisher = {Springer}, title = {{Riemann's Zeta} function: {A} model for quantum chaos?}, year = {1986}, address = {Berlin}, booktitle = {{Quantum Chaos and Statistical Nuclear Physics}}, doi = {10.1007/3-540-17171-1_1}, } @Article{Berry89, author = {Berry, M. V.}, journal = {Inst. Hautes \'Etudes Sci. Publ. Math.}, title = {Stokes{'} phenomenon; smoothing a {Victorian} discontinuity}, year = {1988}, pages = {211--221}, volume = {68}, doi = {10.1007/BF02698550}, } @Article{BerstelPocchiola94, author = {J. Berstel and M. Pocchiola}, journal = {Theor. Comput. Sci.}, title = {Average cost of {Duval's} algorithm for generating {Lyndon} words}, year = {1994}, pages = {415--425}, volume = {132}, doi = {10.1016/0304-3975(94)00013-1}, } @Article{BeTh04, Title = {Freezing solutions of equivariant evolution equations}, Author = {W.-J. Beyn and V. Th\"ummler}, Journal = {SIAM J. Appl. Dyn. Syst.}, Year = {2004}, Pages = {85--116}, Volume = {3}, DOI = {10.1137/030600515} } @Article{BG81, author = {D. J. {Benney} and L. H. {Gustavsson}}, journal = {Stud. Appl. Math.}, title = {A new mechanism for linear and nonlinear hydrodynamic instability}, year = {1981}, pages = {185--209}, volume = {64}, doi = {10.1002/sapm1981643185}, } @Article{BGMWW92, author = {A. Back and J. Guckenheimer and M. R. Myers and F. J. Wicklin and P. A. Worfolk}, title = {{DsTool: Computer} assisted exploration of dynamical systems}, journal = {Notices Amer. Math. Soc.}, year = {1992}, volume = {39}, pages = {303--309}, doi = {10.1.1.49.4297}, } @Article{BGO90, Title = {Bifurcation to chaotic scattering}, Author = {Bleher, S. and Grebogi, C. and Ott, E.}, Journal = {Physica D.}, Year = {1990}, Pages = {87--121}, Volume = {46}, DOI = {10.1016/0167-2789(90)90114-5} } @Book{BH86, title = {{Asymptotic Expansions of Integrals}}, publisher = {Dover}, year = {1986}, author = {N. Bleistein and R. A. Handelsman}, address = {New York}, isbn = {9780486650821}, } @Book{BHLL13, title = {{Zeta functions for two-dimensional shifts of finite type}}, publisher = {Memoirs Amer. Math. Soc.}, year = {2013}, author = {Ban, J.-C. and Hu, W.-G. and Lin, S.-S. and Lin, Y.-H.}, volume = {221}, doi = {10.1090/S0065-9266-2012-00653-8}, } @Book{BHLV03, title = {{Bifurcations in {Hamiltonian} Systems: Computing Singularities by Gr\"obner Bases}}, publisher = {Springer}, year = {2003}, author = {Broer, H. W. and Hoveijn, I. and Lunter, G. A. and Vegter, G.}, address = {New York}, doi = {10.1007/b10414}, } @Article{biham90c, author = {O. Biham and W. Wenzel}, title = {Unstable periodic orbits and the symbolic dynamics of the complex {H\'e}non map}, journal = {Phys. Rev. E}, year = {1990}, volume = {42}, pages = {4639}, doi = {10.1103/physreva.42.4639}, } @Article{BillBoll05, Title = {Invariant densities for skew tent maps}, Author = {Billings, L. and Bollt, E. M.}, Journal = {Chaos Solit. Fract.}, Year = {2001}, Pages = {365}, Volume = {12}, URL = {http://people.clarkson.edu/~bolltem/Papers/csf_2001.pdf} } @Book{Bincer12, Title = {{Lie Groups and Lie Algebras - A Physicist's Perspective}}, Author = {Bincer, A. M.}, Publisher = {Oxford Univ. Press}, Year = {2012}, ISBN = {9780191640087} } @Article{birk, Title = {On the periodic motions of dynamical systems}, Author = {Birkhoff, G. D.}, Journal = {Acta Math.}, Year = {1927}, note = {Reprinted in \refref{ham}}, Pages = {359--379}, Volume = {50}, DOI = {10.1007/BF02421325} } @Article{Birkhoff31, Title = {Proof of the {Ergodic Theorem}}, Author = {Birkhoff, G. D.}, Journal = {Proc. Natl. Acad. Sci. USA}, Year = {1931}, Pages = {656--660}, Volume = {17}, DOI = {10.1073/pnas.17.2.656} } @Book{Birkhoff55, title = {{Dynamical Systems}}, publisher = {Amer. Math. Soc.}, year = {1955}, author = {G. D. Birkhoff}, address = {Providence RI}, url = {http://www.ams.org/online_bks/coll9/}, } @Article{birkoff, Title = {The restricted problem of three bodies}, Author = {G. D. Birkoff}, Journal = {Rend. Circ. Mat. Palermo}, Year = {1915}, Pages = {265--334}, Volume = {39}, DOI = {10.1007/BF03015982} } @Article{BirViv, Title = {Periodic orbits of the sawtooth maps}, Author = {N. Bird and F. Vivaldi}, Journal = {Physica D}, Year = {1988}, Pages = {164--176}, Volume = {30}, DOI = {10.1016/0167-2789(88)90104-2} } @Article{BisPal98, author = {Santanu Pal and Debabrata Biswas}, title = {Symmetry reduction and semiclassical analysis of axially symmetric systems}, journal = {Phys. Rev. E}, year = {1998}, volume = {57}, pages = {1475--1484}, doi = {10.1103/physreve.57.1475}, } @Article{BitCol00, author = {S. Bittanti and P. Colaneri}, journal = {Automatica}, title = {Invariant representations of discrete-time periodic systems}, year = {2000}, pages = {1777--1793}, volume = {36}, doi = {10.1016/S0005-1098(00)00087-X}, } @InBook{BitCol01, author = {Bittanti, S. and Colaneri, P.}, chapter = {{Periodic control}}, pages = {240-- 253}, publisher = {Wiley}, title = {{Periodic control}}, year = {1999}, address = {New York}, isbn = {9780471346081}, volume = {16}, booktitle = {Wiley Encyclopedia of Electrical and Electronics Engineering}, doi = {10.1002/047134608X.W1030}, } @Article{BJNRZ12, Title = {Stability of periodic {Kuramoto--Sivashinsky} waves}, Author = {B. Barker and M. A. Johnson and P. Noble and L. M. Rodrigues and K. Zumbrun}, Journal = {Appl. Math. Lett.}, Year = {2012}, Pages = {824--829}, Volume = {25}, DOI = {10.1016/j.aml.2011.10.026} } @Article{bk, Title = {The spherical model of a ferromagnet}, Author = {Berlin, T. H. and Kac, M.}, Journal = {Phys. Rev.}, Year = {1952}, Pages = {821--835}, Volume = {86}, DOI = {10.1103/PhysRev.86.821} } @Article{BK90, author = {M. V. Berry and J. P. Keating}, title = {A rule for quantizing chaos}, journal = {J. Phys. A}, year = {1990}, volume = {23}, pages = {4839--4849}, doi = {10.1088/0305-4470/23/21/024} } @Article{BK99, Title = {The {Riemann} zeros and eigenvalue asymptotics}, Author = {Berry, M. V. and Keating, J. P.}, Journal = {SIAM Rev.}, Year = {1999}, Pages = {236--266}, Volume = {41}, DOI = {10.1137/S0036144598347497} } @Article{BKL02, Title = {{Ruelle-Perron-Frobenius} spectrum for {Anosov} maps}, Author = {M. Blank and G. Keller and C. Liverani}, Journal = {Nonlinearity}, Year = {2002}, Pages = {1905--1973}, Volume = {15}, DOI = {10.1088/0951-7715/15/6/309} } @Article{bknk, author = {N. Bekki and K. Nozaki}, title = {Formations of spatial patterns and holes in the generalized {Ginzburg-Landau} equation}, journal = {Phys. Lett.}, year = {1985}, volume = {110A}, pages = {133--135}, doi = {10.1016/0375-9601(85)90759-5}, } @Article{bknk83, author = {K. Nozaki and N. Bekki}, title = {Pattern selection and spatiotemporal transition to chaos in the {Ginzburg-Landau} equation}, journal = {Phys. Rev. Lett.}, year = {1983}, volume = {51}, pages = {2171}, doi = {10.1103/physrevlett.51.2171}, } @Article{bknk84, author = {K. Nozaki and N. Bekki}, title = {Exact solutions of the generalized {Ginzburg-Landau} equation}, journal = {J. Phys. Soc. Japan}, year = {1984}, volume = {53}, pages = {1581--1582}, doi = {10.1143/jpsj.53.1581}, } @Article{BKRS96, author = {V. Baladi and A. Kitaev, D. Ruelle and S. Semmes}, title = {Sharp determinants and kneading operators for holomorphic maps}, journal = {Proc. Steklov Inst. of Math.}, year = {1997}, volume = {216}, pages = {186--228}, url = {http://www.ihes.fr/~ruelle/PUBLICATIONS/%5B119%5D.pdf}, } @Book{BKS91, Title = {{Ergodic Theory, Symbolic Dynamics, and Hyperbolic Spaces}}, Author = {Bedford, T. and Keane, M.S. and Series, C.}, Publisher = {Oxford Univ. Press}, Year = {1991}, Address = {Oxford}, ISBN = {9780198533900} } @Book{bl, title = {{Introduction to Numerical Analysis}}, publisher = {Springer}, year = {1983}, author = {J. Stoer and R. Bulirsch}, address = {New York}, doi = {10.1007/978-1-4757-5592-3}, } @Article{BlaKel98, Title = {Random perturbations of chaotic dynamical systems: stability of the spectrum}, Author = {M. Blank and G. Keller}, Journal = {Nonlinearity}, Year = {1998}, Pages = {1351--1364}, Volume = {11}, DOI = {10.1088/0951-7715/11/5/010} } @Book{Blank97, Title = {{Discreteness and Continuity in Problems of Chaotic Dynamics}}, Author = {Blank, M .L.}, Publisher = {Amer. Math. Soc.}, Year = {1997}, Address = {Providence RI}, ISBN = {9780821897751} } @Article{BlCeJVi03, author = {M. Blasone and E. Celeghini and P. Jizba and G. Vitiello}, title = {Quantization, group contraction and zero point energy}, journal = {Phys. Lett. A}, year = {2003}, volume = {310}, pages = {393--399}, doi = {10.1016/S0375-9601(03)00374-8}, } @Article{Bleher92, Title = {Statistical properties of two-dimensional periodic {Lorentz} gas with infinite horizon}, Author = {P. M. Bleher}, Journal = {J. Stat. Phys.}, Year = {1992}, Pages = {479--497}, Volume = {66}, DOI = {10.1007/BF01060071} } @Article{BlGrPaVi96, author = {M. Blasone and E. Graziano and O. K. Pashaev and G. Vitiello}, title = {Dissipation and topologically massive gauge theories in the pseudo-euclidean plane}, journal = {Ann. Phys. (N.Y.)}, year = {1996}, volume = {252}, pages = {115--132}, doi = {10.1006/aphy.1996.0126}, } @Article{BlJVi01, Title = {Dissipation and quantization}, Author = {Blasone, M. and Jizba, P. and Vitiello, G.}, Journal = {Phys. Lett. A}, Year = {2001}, Pages = {205--210}, Volume = {287}, DOI = {10.1016/S0375-9601(01)00474-1} } @Article{BlMaLo05, author = {H. M. Blackburn and F. Marques and Lopez, J. M.}, title = {Symmetry breaking of two-dimensional time-periodic wakes}, journal = {J. Fluid Mech.}, year = {2005}, volume = {522}, pages = {395--411}, doi = {10.1017/S0022112004002095} } @Article{BlMaZe05, Title = {Nonholonomic dynamics}, Author = {Bloch, A. M. and Marsden, J. E. and Zenkov, D. V.}, Journal = {Notices Amer. Math. Soc.}, Year = {2005}, Pages = {324--333}, Volume = {52}, URL = {http://www.ams.org/notices/200503/fea-bloch.pdf} } @Article{BLMS15, author = {R. Barrio and M. Lefranc and M. A. Mart{\'i}nez and S. Serrano}, title = {Symbolic dynamical unfolding of spike-adding bifurcations in chaotic neuron models}, journal = {Europhys. Lett.}, year = {2015}, volume = {109}, pages = {20002}, doi = {10.1209/0295-5075/109/20002}, } @Article{BLMS91, author = {Bivins, R. L. and Louck, J. D. and Metropolis, N. and Stein, M. L.}, journal = {Physica D}, title = {Classification of all cycles of the parabolic map}, year = {1991}, pages = {3--27}, volume = {51}, doi = {10.1016/0167-2789(91)90218-X}, } @Article{BLOFDMCFD04, Title = {Ultrathin epitaxial graphite: {2D} electron gas properties and a route toward graphene-based nanoelectronics}, Author = {Berger, C. and Song, Z. and Li, T. and Li, X. and Ogbazghi, A. Y. and Feng, R. and Dai, Z. and Marchenkov, A. N. and Conrad, E. H. and First, P. N. and De Heer, W. A.}, Journal = {J. Phys. Chem. B}, Year = {2004}, Pages = {19912--19916}, Volume = {108}, DOI = {10.1021/jp040650f} } @Article{BlSrViWi98, author = {M. Blasone and Y. N. Srivastava and G. Vitiello and A. Widom}, title = {Phase coherence in quantum {Brownian} motion}, journal = {Ann. Phys. (N.Y.)}, year = {1998}, volume = {267}, pages = {61--74}, doi = {10.1006/aphy.1998.5811}, } @Article{Bluman07, author = {G. Bluman}, title = {Connections between symmetries and conservation laws}, journal = {SIGMA}, year = {2005}, volume = {1}, pages = {011}, doi = {10.3842/SIGMA.2005.011}, } @Book{BlumanAnco02, title = {{Symmetry and Integration Methods for Differential Equations}}, publisher = {Springer}, year = {2002}, author = {G. W. Bluman and S. C. Anco}, address = {New York}, doi = {10.1007/b97380}, } @Book{BlumanSDE89, title = {{Symmetries and Differential Equations}}, publisher = {Springer}, year = {1989}, author = {G. W. Bluman and S. Kumei}, address = {New York}, doi = {10.1007/978-1-4757-4307-4}, } @Article{BMS71, Title = {Aperiodic behavior of a non-linear oscillator}, Author = {N. H. Baker and D. W. Moore and E. A. Spiegel}, Journal = {Quatr. J. Mech. and Appl. Math.}, Year = {1971}, Pages = {391--422}, Volume = {24}, DOI = {10.1093/qjmam/24.4.391} } @Article{BoCvJe88, Title = {Fractal ``aggregates" in the complex plane}, Author = {Bohr, T. and Cvitanovi{\'c}, P. and Jensen, M. H.}, Journal = {Europhys. Lett.}, Year = {1988}, Pages = {445--450}, Volume = {6}, DOI = {10.1209/0295-5075/6/5/012} } @Article{BocZah07, Title = {The distribution of the free path lengths in the periodic two-dimensional {Lorentz} gas in the small-scatterer limit}, Author = {Boca, F. P. and Zaharescu, A.}, Journal = {Commun. Math. Phys.}, Year = {2007}, Pages = {425--471}, Volume = {269}, DOI = {10.1007/s00220-006-0137-7} } @Article{BoDuSchm08, Title = {Trace formula for dielectric cavities: { General} properties}, Author = {Bogomolny, E. and Dubertrand, R. and Schmit, C.}, Journal = {Phys. Rev. E}, Year = {2008}, Pages = {056202}, Volume = {78}, DOI = {10.1103/PhysRevE.78.056202} } @Article{BoGoWe98, Title = {On the distribution of free path lengths for the periodic {Lorentz} gas}, Author = {J. Bourgain and F. Golse and B. Wennberg}, Journal = {Commun. Math. Phys.}, Year = {1998}, Pages = {491--508}, Volume = {190}, DOI = {10.1007/s002200050249} } @Article{BoGuHe15, Title = {On diffeomorphisms of compact 2-manifolds with all nonwandering points being periodic}, Author = {Boyd, S. and Guirao, J. L. G. and Hero, M.}, Journal = {Int. J. Bifur. Chaos}, Year = {2015}, Pages = {1540020}, Volume = {25}, DOI = {10.1142/S0218127415400209}, } @Book{bohr98tur, author = {T. Bohr and M. H. Jensen and G. Paladin and A. Vulpiani}, publisher = {Cambridge Univ. Press}, title = {{Dynamical Systems Approach to Turbulence}}, year = {1998}, address = {Cambridge UK}, doi = {10.1017/cbo9780511599972}, } @Article{bollt07, author = {Bollt, E.}, title = {Attractor modeling and empirical nonlinear model reduction of dissipative dynamical systems}, journal = {Int. J. Bifur. Chaos}, year = {2007}, volume = {17}, pages = {1199--1219}, doi = {10.1142/s021812740701777x}, } @Book{BoonYip80, title = {{Molecular Hydrodynamics}}, publisher = {Dover}, year = {1991}, author = {J.-P. Boon and S. Yip}, address = {New York}, doi = {10.1016/b0-12-227410-5/00458-0}, } @Article{BoPo10, Title = {Covariant {Lyapunov} vectors for rigid disk systems}, Author = {Bosetti, H. and Posch, H. A.}, Journal = {Chem. Phys.}, Year = {2010}, Pages = {296--308}, Volume = {375}, DOI = {10.1016/j.chemphys.2010.06.010} } @Article{BoRa95, author = {Botina, J. and Rabitz, H.}, journal = {Phys. Rev. Lett.}, title = {Finding regular orbits}, year = {1995}, pages = {2948--2951}, volume = {75}, doi = {10.1103/PhysRevLett.75.2948}, } @Book{Born27, title = {{Vorlesungen {\"u}ber Atommechanik}}, publisher = {Ungar Publishing}, year = {1927}, author = {M. Born}, address = {New York}, note = {English Translation: The Mechanics of the Atom}, doi = {10.1007/978-3-642-61898-7}, } @Article{BoSeSt86, author = {H.P. Boehm and R. Setton and E. Stumpp}, journal = {Carbon}, title = {Nomenclature and terminology of graphite intercalation compounds}, year = {1986}, pages = {241--245}, volume = {24}, doi = {10.1016/0008-6223(86)90126-0}, } @Article{BoSmWi36, Title = {Theory of {Brillouin} zones and symmetry properties of wave functions in crystals}, Author = {Bouckaert, L. P. and Smoluchowski, R. and Wigner, E.}, Journal = {Phys. Rev.}, Year = {1936}, Pages = {58--67}, Volume = {50}, DOI = {10.1103/PhysRev.50.58} } @Book{Botti89, author = {Ottino, J. M.}, publisher = {Cambridge Univ. Press}, title = {{The Kinematics of Mixing: Stretching, Chaos and Transport}}, year = {1989}, address = {Cambridge UK}, isbn = {9780521368780}, } @Article{Bount81, Title = {On the stability of periodic orbits of two-dimensional mappings}, Author = {Bountis, T. and Helleman, R. H. G.}, Journal = {J. Math. Phys}, Year = {1981}, Pages = {1867--1877}, Volume = {22}, DOI = {10.1063/1.525159} } @Article{BoWe14, author = {Borthwick, D. and {Weich}, T.}, journal = {J. Spectral Theory}, title = {Symmetry reduction of holomorphic iterated function schemes and factorization of {Selberg} zeta functions}, year = {2016}, pages = {267--329}, volume = {6}, doi = {10.4171/jst/125}, } @Book{bowen, title = {{Equilibrium States and the Ergodic Theory of {Anosov} Diffeomorphisms}}, publisher = {Springer}, year = {1975}, author = {R. Bowen}, isbn = {9783540776956}, address = {New York}, doi = {10.1007/bfb0081279}, } @Article{Bowen70, Title = {{Markov} partitions for {Axiom A} diffeomorphisms}, Author = {Bowen, R.}, Journal = {Amer. J. Math.}, Year = {1970}, Pages = {725--747}, Volume = {92}, DOI = {10.2307/2373370} } @Article{Bowen71, author = {R. Bowen}, journal = {Trans. Amer. Math. Soc.}, title = {Periodic points and measures for {Axiom A} diffeomorphisms}, year = {1971}, pages = {377--397}, volume = {154}, doi = {10.2307/1995452}, } @Article{Bowen72, Title = {Periodic orbits for hyperbolic flows}, Author = {R. Bowen}, Journal = {Amer. J. Math.}, Year = {1972}, Pages = {1--30}, Volume = {94}, DOI = {10.2307/2373590} } @Article{Bowen73, Title = {Symbolic dynamics for hyperbolic flows}, Author = {R. Bowen}, Journal = {Amer. J. Math.}, Year = {1973}, Pages = {429--460}, Volume = {95}, DOI = {10.2307/2373793} } @Inproceedings{BowLan70, author = {Bowen, R. and Lanford, O.}, title = {Zeta functions of restrictions of the shift transformation}, booktitle = {{Global Analysis (Proc. Sympos. Pure Math., Berkeley, CA, 1968)}}, year = {1970}, editor = {S.-S. Chern and S. Smale}, volume = {1}, isbn = {9780821814147}, pages = {43--50}, address = {Providence, RI}, publisher = {Amer. Math. Soc.}, doi = {10.1090/pspum/014/9985}, } @Article{Boy84, Title = {On the significance of absolutely continuous invariant measures}, Author = {A. Boyarsky}, Journal = {Physica D}, Year = {1984}, Pages = {130--146}, Volume = {11}, DOI = {10.1016/0167-2789(84)90439-1} } @Article{Boy88, Title = {A matrix method for estimating the {Liapunov} exponent of one-dimensional systems}, Author = {Boyarsky, A.}, Journal = {J. Stat. Phys.}, Year = {1988}, Pages = {213--229}, Volume = {50}, DOI = {10.1007/BF01022993} } @Book{BoyGor97, Title = {{Laws of Chaos: Invariant Measures and Dynamical Systems in One Dimension}}, Author = {A. Boyarsky and P. G\'ora}, Publisher = {Birkh\"{a}user}, Year = {1997}, Address = {Boston}, ISBN = {9781461220244} } @Article{BoySka79, Title = {On a class of transformations which have unique absolutely continuous invariant measures}, Author = {A. Boyarsky and M. Skarowsky}, Journal = {Trans. Amer. Math. Soc.}, Year = {1979}, Pages = {243--262}, Volume = {255}, DOI = {10.1090/S0002-9947-1979-0542879-2} } @Article{BPPV84, Title = {On the multifractal nature of fully developed turbulence and chaotic systems}, Author = {R. Benzi and G. Paladin, G. Parisi and A. Vulpiani}, Journal = {J. Phys. A}, Year = {1984}, Pages = {3521}, Volume = {17}, DOI = {10.1088/0305-4470/17/18/021} } @Article{BPTV88, Title = {Generalized dimensions, entropies, and {Liapunov} exponents from the pressure function for strange sets}, Author = {Bessis, D. and Paladin, G. and Turchetti, G. and Vaienti, S.}, Journal = {J. Stat. Phys.}, Year = {1988}, Pages = {109--134}, Volume = {51}, DOI = {10.1007/BF01015323} } @Article{BQT91, Title = {Feigenvalues for {Mandelsets}}, Author = {K. M. Briggs and G. R. W. Quispel and C. J. Thompson}, Journal = {J. Phys. A}, Year = {1991}, Pages = {3363--3368}, Volume = {24}, DOI = {10.1088/0305-4470/24/14/023} } @Article{BR56, author = {Balatoni, J. and R{\'e}nyi, A.}, journal = {Publ. Math. Inst. Hung. Acad. Sci.}, title = {Remarks on entropy}, year = {1956}, pages = {9--40}, volume = {1}, } @Article{BR94, Title = {An extension of the theorem of {Milnor and Thurston} on the zeta functions of interval maps}, Author = {Baladi, V. and Ruelle, D.}, Journal = {Ergod. Theor. Dynam. Syst.}, Year = {1994}, Pages = {621--632}, Volume = {14}, DOI = {10.1017/S0143385700008087} } @Article{BR96, author = {Baladi, V. and Ruelle, D.}, title = {Sharp determinants}, journal = {Inv. Math.}, year = {1996}, volume = {123}, pages = {553--574}, doi = {10.1007/s002220050040}, } @Article{BrackMurthy:93, author = {M. Brack and R. K. Bhaduri and J. Law and M. V. N. Murthy}, title = {Analytic formulas for periodic orbits in {He{\'e}non-Heiles}}, journal = {Phys. Rev. Lett.}, year = {1993}, volume = {70}, pages = {568--571}, doi = {10.1103/PhysRevLett.70.568}, } @InCollection{brand03, author = {Brandenburg, A.}, booktitle = {{Advances in Nonlinear Dynamos}}, publisher = {Taylor \& Francis}, title = {Computational aspects of astrophysical {MHD} and turbulence}, year = {2003}, address = {London}, editor = {A. Ferriz-Mas and M. N{\'{u}\~{n}ez}}, pages = {269--344}, doi = {10.1201/9780203493137.ch9}, } @Incollection{breakt, author = {G. Casati and B. V. Chirikov and F. M. Izrailev and J. Ford}, title = {Stochastic behavior of a quantum pendulum under a periodic perturbation}, booktitle = {{Stochastic Behaviour in Classical and Quantum {Hamiltonian} Systems}}, publisher = {Springer}, year = {1979}, editor = {G. Casati and J. Ford}, isbn = {978-3-540-09120-2}, pages = {334--352}, doi = {10.1007/BFb0021757}, } @Book{Bredon72, Title = {{Introduction to Compact Transformation Groups}}, Author = {G. Bredon}, Publisher = {Academic}, Year = {1972}, Address = {New York}, ISBN = {9780080873596} } @Article{BrEllGBAHo10, Title = {Un-reduction}, Author = {{Bruveris}, M. and {Ellis}, D. C. P. and {Gay-Balmaz}, F. and {Holm}, D. D.}, Journal = {J. Geom. Mech.}, Year = {2011}, Pages = {363--387}, Volume = {3}, DOI = {10.3934/jgm.2011.3.363} } @Article{Bri96, Title = {Science of chaos or chaos in science?}, Author = {Bricmont, J.}, Journal = {Ann. New York Acad. Sci.}, Year = {1995}, Pages = {131--175}, Volume = {775}, DOI = {10.1111/j.1749-6632.1996.tb23135.x} } @Article{Bridg91, Title = {The spin of a bouncing `superball'}, Author = {R. Bridges}, Journal = {Phys. Educ.}, Year = {1991}, Pages = {350--354}, Volume = {26}, DOI = {10.1088/0031-9120/26/6/003} } @Misc{Bridges_priv, author = {T. J. Bridges}, note = {Private communication}, } @Article{Bridges08, author = {T. J. Bridges}, title = {Degenerate relative equilibria, curvature of the momentum map, and homoclinic bifurcation}, journal = {J. Diff. Eqn.}, year = {2008}, volume = {244}, pages = {1629--1674}, doi = {10.1016/j.jde.2008.01.019}, } @Article{Briggs89, Title = {How to calculate the {Feigenbaum} constants on your {PC}}, Author = {Briggs, K.}, Journal = {Austral. Math. Soc. Gaz.}, Year = {1989}, Pages = {89-92}, Volume = {16} } @Article{Briggs91, Title = {A precise calculation of the {Feigenbaum} constants}, Author = {Briggs, K.}, Journal = {Mathematics of Computation}, Year = {1991}, Pages = {435--439}, Volume = {57}, DOI = {10.1090/S0025-5718-1991-1079009-6} } @Article{BriPer05, author = {Bridy, A. and P{\'e}rez, R. A.}, journal = {Nonlinearity}, title = {A count of maximal small copies in {Multibrot} sets}, year = {2005}, pages = {1945--1953}, volume = {18}, doi = {10.1088/0951-7715/18/5/004}, } @Incollection{BrKevr96, author = {Brown, H. S. and Kevrekidis, I. G.}, title = {Modulated traveling waves for the {Kuramoto-Sivashinsky} equation}, booktitle = {{Pattern Formation: Symmetry Methods and Applications}}, publisher = {AMS}, year = {1996}, editor = {J. Chadam and M. Golubitsky and W. Langford and Brian Wetton}, isbn = {978-0-8218-0256-4}, pages = {45--66}, address = {Providence, RI}, doi = {10.1090/fic/005/03}, } @Article{bro94sur, author = {G. Brodin and J. Lundberg}, title = {Nonlinear surface waves in a plasma with a diffuse boundary}, journal = {Phys. Plasmas}, year = {1994}, volume = {1}, pages = {96}, doi = {10.1063/1.870465}, } @Misc{Broadhurst99, Title = {Feigenbaum constants to 1018 decimal places}, Author = {D. Broadhurst}, Year = {1999}, URL = {http://www.plouffe.fr/simon/constants/feigenbaum.txt} } @Book{BroDie85, title = {{Representations of Compact {Lie} Groups}}, publisher = {Springer}, year = {1985}, author = {Br{\"o}cker, T. and tom Dieck, T.}, volume = {98}, address = {New York}, doi = {10.1007/978-3-662-12918-0}, } @Article{broer_quasi-periodic_2007, author = {H. W. Broer and M. C. Ciocci and H. Hanssmann}, title = {The quasi-periodic reversible {Hopf} bifurcation}, journal = {Int. J. Bifur. Chaos}, year = {2007}, volume = {17}, pages = {2605--2623}, doi = {10.1142/s021812740701866x}, } @Article{Broer90, Title = {Unfoldings and bifurcations of quasi-periodic tori. {I: Unfolding} of quasi-periodic tori}, Author = {Broer, H. W. and G. B. Huitema and F. Takens and B. L. J. Braaksma}, Journal = {Memoirs Amer. Math. Soc.}, Year = {1990}, volume={83}, pages={1--82}, DOI = {10.1090/memo/0421}, } @Article{broer97, author = {H. W. Broer and H. M. Osinga and G. Vegter}, title = {Algorithms for computing {N}ormally {H}yperbolic {I}nvariant {M}anifolds}, journal = {Z. Angew. Math. Phys.}, year = {1997}, volume = {48}, pages = {480}, doi = {10.1007/s000330050044}, } @Article{BrOgYuRe05, author = {M. Brack and M. \"Ogren and Y. Yu and S. M. Reimann}, title = {Uniform semiclassical trace formula for {$U(3) \to SO(3)$} symmetry breaking}, journal = {J. Phys. A}, year = {2005}, volume = {38}, pages = {9941--9967}, doi = {10.1088/0305-4470/38/46/004}, } @Article{bronski2005, Title = {Uncertainty estimates and {$L_2$} bounds for the {Kuramoto-Sivashinsky} equation}, Author = {J. C. Bronski and T. N. Gambill}, Journal = {Nonlinearity}, Year = {2006}, Pages = {2023--2039}, Volume = {19}, DOI = {10.1088/0951-7715/19/9/002} } @Book{BroTak10, title = {{Dynamical Systems and Chaos}}, publisher = {Springer}, year = {2010}, author = {Broer, H. and Takens, F.}, isbn = {9781441968708}, address = {New York}, doi = {10.1007/978-1-4419-6870-8}, } @Article{Broucke69, Title = {Stability of periodic orbits in the elliptic, restricted three-body problem}, Author = {R. Broucke}, Journal = {AIAA Journal}, Year = {1969}, Pages = {1003--1009}, Volume = {7}, DOI = {10.2514/3.5267} } @Article{Broucke75, author = {R. Broucke}, title = {On relative periodic solutions of the planar general three-body problem}, journal = {Celestial Mech. Dynam. Astronom.}, year = {1975}, volume = {12}, pages = {439--462}, doi = {10.1007/BF01595390} } @Article{Brown81, author = {Brown, A.}, journal = {J. Austral. Math. Soc. Ser. B}, title = {Equations for periodic solutions of a logistic difference equation}, year = {1981}, pages = {78--94}, volume = {23}, doi = {10.1017/S0334270000000072}, } @Article{brucks, Title = {{MSS} sequences, colorings of necklaces, and periodic points of {$f(z) = z^2 $-$ 2$}}, Author = {K. M. Brucks}, Journal = {Adv. Appl. Math.}, Year = {1987}, Pages = {434--445}, Volume = {8}, DOI = {10.1016/0196-8858(87)90020-0} } @Article{BSM, author = {B. Eckhardt}, journal = {Phys. Lett. A}, title = {Periodic orbits and diffusion in standard maps}, year = {1993}, pages = {411}, volume = {172}, doi = {10.1016/0375-9601(93)90231-n}, } @Article{bst, author = {C. S. Hsu and M. C. Kim}, title = {Construction of maps with generating partitions for entropy evaluation}, journal = {Phys. Rev. A}, year = {1985}, volume = {31}, pages = {3253--3265}, doi = {10.1103/PhysRevA.31.3253} } @Article{BSTV97, author = {F. Brini and S. Siboni and G. Turchetti and S. Vaienti}, title = {Decay of correlations for the automorphism of the torus {$T^2$}}, journal = {Nonlinearity}, year = {1997}, volume = {10}, pages = {1257--1268}, doi = {10.1088/0951-7715/10/5/012} } @Article{BSW36, author = {L. P. Bouckaert and R. Smoluchowski and E. P. Wigner}, journal = {Phys. Rev.}, title = {Theory of {Brillouin} zones and symmetry properties of wave functions in crystals}, year = {1936}, pages = {58--67}, volume = {50}, doi = {10.1103/PhysRev.50.58}, } @Article{BTBmaw03, author = {L. Brusch and A. Torcini and M. B{\"{a}}r}, title = {Nonlinear analysis of the {Eckhaus} instability: {Modulated} amplitude waves and phase chaos with nonzero average phase gradient}, journal = {Physica D}, year = {2003}, volume = {174}, pages = {152--167}, doi = {10.1016/s0167-2789(02)00688-7}, } @Article{BTHmaw01, Title = {Modulated amplitude waves and defect formation in the one-dimensional complex {Ginzburg-Landau} equation}, Author = {L. Brusch and A. Torcini and M. van Hecke and M. G. Zimmermann and M. B{\"{a}}r}, Journal = {Physica D}, Year = {2001}, Pages = {127--148}, Volume = {160}, DOI = {10.1016/S0167-2789(01)00355-4} } @Article{BuBoCvSi14, author = {Budanur, N. B. and Borrero-Echeverry, D. and Cvitanovi{\'c}, P.}, journal = {Chaos}, title = {Periodic orbit analysis of a system with continuous symmetry - {A} tutorial}, year = {2015}, pages = {073112}, volume = {25}, doi = {10.1063/1.4923742}, } @PhdThesis{BudanurThesis, author = {Budanur, N. B.}, title = {{Exact Coherent Structures in Spatiotemporal Chaos: From Qualitative Description to Quantitative Predictions}}, school = {School of Physics, Georgia Inst. of Technology}, year = {2015}, address = {Atlanta}, url = {http://ChaosBook.org/projects/theses.html}, } @Article{budapest, Title = {Phase transitions associated with dynamical properties of chaotic systems}, Author = {P. Sz{\'e}pfalusy and T. T{\'e}l, A. Csord{\'a}s and Z. Kov{\'a}cs}, Journal = {Phys. Rev. A}, Year = {1987}, Pages = {3525--3528}, Volume = {36}, DOI = {10.1103/PhysRevA.36.3525} } @Article{BudCvi14, Title = {Reduction of the {SO(2)} symmetry for spatially extended dynamical systems}, Author = {Budanur, N. B. and Cvitanovi{\'c}, P. and Davidchack, R. L. and Siminos, E.}, Journal = {Phys. Rev. Lett.}, Year = {2015}, Pages = {084102}, Volume = {114}, DOI = {10.1103/PhysRevLett.114.084102} } @Article{BudCvi15, author = {Budanur, N. B. and Cvitanovi\'c, P.}, title = {Unstable manifolds of relative periodic orbits in the symmetry-reduced state space of the {Kuramoto-Sivashinsky} system}, journal = {J. Stat. Phys.}, year = {2015}, volume = {167}, pages = {636--655}, doi = {10.1007/s10955-016-1672-z}, } @Article{Buff99, Title = {Geometry of the {Feigenbaum} map}, Author = {X. Buff}, Journal = {Conform. Geom. Dyn.}, Year = {1999}, Pages = {79--101}, Volume = {3}, DOI = {10.1090/S1088-4173-99-00031-4} } @Article{buni74, Title = {On ergodic properties of certain billiards}, Author = {Bunimovich, L. A.}, Journal = {Funct. Anal. Appl.}, Year = {1974}, Pages = {254--255}, Volume = {8}, DOI = {10.1007/BF01075700} } @Article{buni79, Title = {On the ergodic properties of nowhere dispersing billiards}, Author = {Bunimovich, L. A.}, Journal = {Commun. Math. Phys.}, Year = {1979}, Pages = {295--312}, Volume = {65}, DOI = {10.1007/BF01197884} } @Article{Bunimovich85, Title = {Decay of correlations in dynamical systems with chaotic behavior}, Author = {Bunimovich, L. A.}, Journal = {Sov. Phys. JETP}, Year = {1985}, Pages = {842--852}, Volume = {62}, URL = {http://jetp.ac.ru/cgi-bin/dn/e_062_04_0842.pdf} } @Article{BunM, Title = {Variational principle for periodic trajectories of hyperbolic billiards}, Author = {L. A. Bunimovich}, Journal = {Chaos}, Year = {1995}, Pages = {349--355}, Volume = {5}, DOI = {10.1063/1.166105} } @Article{BunSin80, Title = {{Markov} partitions for dispersed billiards}, Author = {Bunimovich, L. A. and Sinai, Ya. G.}, Journal = {Commun. Math. Phys.}, Year = {1980}, Note = {Erratum, ibid. {\bf 107}, 357 (1986)}, Pages = {247--280}, Volume = {78}, DOI = {10.1007/BF01942372} } @Article{BunSin81, Title = {Statistical properties of {Lorentz} gas with periodic configuration of scatterers}, Author = {Bunimovich, L. A. and Sinai, Ya. G.}, Journal = {Commun. Math. Phys.}, Year = {1981}, Pages = {479--497}, Volume = {78}, DOI = {10.1007/BF02046760} } @Article{BuSiCh90, author = {Bunimovich, L. A. and Sinai, Ya. G. and Chernov, N. I.}, journal = {Russ. Math. Surv.}, title = {{Markov} partitions for two-dimensional hyperbolic billiards}, year = {1990}, pages = {105--152}, volume = {45}, doi = {10.1070/RM1990v045n03ABEH002355}, } @Article{Busse04, author = {F. H. Busse}, title = {Visualizing the dynamics of the onset of turbulence}, journal = {Science}, year = {2004}, volume = {305}, pages = {1574--1575}, doi = {10.1126/science.1102824}, } @Book{ByFu92, title = {{Mathematics of Classical and Quantum Physics}}, publisher = {Dover}, year = {1992}, author = {F. W. Byron and R. W. Fuller}, isbn = {9780486671642}, address = {New York}, } @Article{BZMmaw00, Title = {Modulated amplitude waves and the transition from phase to defect chaos}, Author = {L. Brusch and M. G. Zimmermann and M. van Hecke and M. B{\"{a}}r and A. Torcini}, Journal = {Phys. Rev. Lett.}, Year = {2000}, Pages = {86--89}, Volume = {85}, DOI = {10.1103/PhysRevLett.85.86} } @Article{C02, author = {S. J. Chapman}, title = {Subcritical transition in channel flows}, journal = {J. Fluid Mech.}, year = {2002}, volume = {451}, pages = {35--97}, doi = {10.1017/s0022112001006255}, } @Misc{C77, Title = {Classical and exceptional {Lie} algebras as invariance algebras}, Author = {P. Cvitanovi{\'c}}, Note = {{Oxford} {Univ.} preprint 40/77, unpublished.}, Year = {1977}, URL = {http://birdtracks.eu/refs/OxfordPrepr.pdf} } @Misc{CaCaKi63, author = {Cash, J. and Carter Cash, J. and Kilgore, M.}, title = {{The Ring of Fire}}, year = {1963}, address = {New York}, publisher = {Columbia Records}, url = {https://en.wikipedia.org/wiki/Ring_of_Fire_(song)}, } @Article{CaEpRu82, author = {M. Campanino and H. Epstein and D. Ruelle}, title = {On {Feigenbaum}'s functional equation {$g \circ g(\lambda x) + \lambda g(x) = 0$}}, journal = {Topology}, year = {1982}, volume = {21}, pages = {125--129}, doi = {10.1016/0040-9383(82)90001-5}, } @Article{CagGol03, author = {E. Caglioti and F. Golse}, title = {On the distribution of free path lengths for the periodic {Lorentz} gas {III}}, journal = {Commun. Math. Phys.}, year = {2003}, volume = {236}, pages = {199--221}, doi = {10.1007/s00220-003-0825-5}, } @Article{CagGol08, author = {Caglioti, E. and Golse, F.}, title = {The {Boltzmann-Grad} limit of the periodic {Lorentz} gas in two space dimensions}, journal = {Compt. Rend. Acad. Sci., Math. (Paris)}, year = {2008}, volume = {346}, pages = {477--482}, doi = {10.1016/j.crma.2008.01.016}, } @Article{CagGol10, Title = {On the {Boltzmann-Grad} limit for the two dimensional periodic {Lorentz} gas}, Author = {Caglioti, E. and Golse, F.}, Journal = {J. Stat. Phys.}, Year = {2010}, Pages = {264--317}, Volume = {141}, DOI = {10.1007/s10955-010-0046-1} } @Article{CamEps81, author = {Campanino, M. and Epstein, H.}, title = {On the existence of {Feigenbaum's} fixed point}, journal = {Commun. Math. Phys.}, year = {1981}, volume = {79}, pages = {261--302}, doi = {10.1007/BF01942063} } @Article{camporeale06, author = {E. Camporeale and G. L. Delzanno and G. Lapenta and W. Daughton}, title = {New approach for the study of linear {Vlasov} stability of inhomogeneous systems}, journal = {Phys. Plasmas}, year = {2006}, volume = {13}, pages = {092110}, doi = {10.1063/1.2345358}, } @Book{Canuto88, title = {{Spectral Methods in Fluid Dynamics}}, publisher = {Springer}, year = {1988}, author = {C. Canuto and M. Y. Hussaini and A. Quateroni and T. A. Zhang}, address = {New York}, doi = {10.1007/978-3-642-84108-8}, } @Article{CaPe84, Title = {Regular and chaotic motion in some quartic potentials}, Author = {A. Carnegie and I. C. Percival}, Journal = {J. Phys. A}, Year = {1984}, Pages = {801}, Volume = {17}, DOI = {10.1088/0305-4470/17/4/020} } @Article{car88, author = {F. Cariello and M. Tabor}, title = {{P}ainlev{\'e} expansions for nonintegrable evolution equations}, journal = {Physica D}, year = {1989}, volume = {39}, pages = {77}, doi = {10.1016/0167-2789(89)90040-7}, } @Article{CaRa12, Title = {Classification of symmetric periodic trajectories in ellipsoidal billiards}, Author = {Casas, P. S. and Ram{\'i}rez-Ros, R.}, Journal = {Chaos}, Year = {2012}, Pages = {026110}, Volume = {22}, DOI = {10.1063/1.4706003} } @Article{CarCha04, Title = {Covariant analysis of {Newtonian} multi-fluid models for neutron stars {I: Milne-Cartan} structure and variational formulation}, Author = {Carter, B. and Chamel, N.}, Journal = {Int. J. Mod. Phys. D}, Year = {2004}, Pages = {291--325}, Volume = {13}, DOI = {10.1142/S0218271804004542} } @Article{carl97int, Title = {Cycle expansions for intermittent diffusion}, Author = {Dettmann, C. P. and Cvitanovi{\'c}, P.}, Journal = {Phys. Rev. E}, Year = {1997}, Pages = {6687--6692}, Volume = {56}, DOI = {10.1103/PhysRevE.56.6687} } @Article{CarLit45, author = {M. L. Cartwright and J. E. Littlewood}, title = {On non-linear differential equations of the second order}, journal = {J. London Math. Soc.}, year = {1945}, volume = {20}, pages = {180--189}, doi = {10.1112/jlms/s1-20.3.180}, } @Article{CarMei, Title = {Rigorously diffusive deterministic map}, Author = {J. R. Cary and J. D. Meiss}, Journal = {Phys. Rev. A}, Year = {1981}, Pages = {2664--2668}, Volume = {24}, DOI = {10.1103/PhysRevA.24.2664} } @Book{CartanMF, title = {{La M{\'e}thode du Rep\`ere Mobile, la Th{\'e}orie des Groupes Continus, et les Espaces G{\'e}n{\'e}ralis{\'e}s}}, publisher = {Hermann}, year = {1935}, author = {Cartan, \'E.}, volume = {5}, series = {{Expos{\'e}s} de {G{\'e}om{\'e}trie}}, address = {Paris}, } @Article{Carvalho99, Title = {Pruning fronts and the formation of horseshoes}, Author = {de Carvalho, A.}, Journal = {Ergod. Theor. Dynam. Syst.}, Year = {1999}, Pages = {851--894}, Volume = {19}, DOI = {10.1017/S0143385799133972} } @Article{Cassanas05a, author = {Roch Cassanas}, title = {Reduced {Gutzwiller} formula with symmetry: {C}ase of a finite group}, journal = {J. Math. Phys.}, year = {2006}, volume = {47}, pages = {042102}, doi = {10.1063/1.2184890}, } @Article{Cassanas05b, author = {R. Cassanas}, title = {Reduced {Gutzwiller} formula with symmetry: {Case} of a {Lie} group}, journal = {J. Math. Pures et Appl.}, year = {2006}, volume = {85}, pages = {719--742}, doi = {10.1016/j.matpur.2005.11.003}, } @Article{Casselman05, author = {Casselman, B.}, journal = {Notices Amer. Math. Soc.}, title = {Picturing the horseshoe map}, year = {2005}, pages = {518--519}, volume = {52}, url = {http://www.ams.org/notices/200505/comm-casselman.pdf}, } @Misc{Casselman06, author = {Casselman, B.}, title = {Simple chaos - the {H{\'e}non} map}, year = {2013}, note = {Amer. Math. Soc. Feature Column}, url = {http://www.ams.org/samplings/feature-column/fcarc-henon}, } @Article{CastLess13, Title = {Rigorous numerics in {Floquet} theory: computing stable and unstable bundles of periodic orbits}, Author = {Castelli, R. and Lessard, J.}, Journal = {SIAM J. Appl. Dyn. Syst.}, Year = {2013}, Pages = {204--245}, Volume = {12}, DOI = {10.1137/120873960} } @Article{Cattell2000, author = {K. Cattell and F. Ruskey and J. Sawada and M. Serra and C. R. Miers}, title = {Fast algorithms to generate necklaces, unlabeled necklaces, and irreducible polynomials over {GF(2)}}, journal = {J. Algorithms}, year = {2000}, volume = {37}, pages = {267--282}, doi = {10.1006/jagm.2000.1108}, } @Article{CB92, Title = {Three-dimensional convection in a horizontal layer subjected to constant shear}, Author = {R. M. Clever and F. H. Busse}, Journal = {J. Fluid Mech.}, Year = {1992}, Pages = {511--527}, Volume = {234}, DOI = {10.1017/S0022112092000892} } @Article{CB97, Title = {Tertiary and quaternary solutions for plane {Couette} flow}, Author = {Clever, R. M. and Busse, F. H.}, Journal = {J. Fluid Mech.}, Year = {1997}, Pages = {137--153}, Volume = {344}, DOI = {10.1017/S0022112097005818} } @InCollection{CBcontinuous, author = {P. Cvitanovi{\'c}}, title = {Relativity for cyclists}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2020}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/paper.shtml#continuous}, } @InCollection{CBconverg, author = {R. Artuso and H. H. Rugh and P. Cvitanovi{\'c}}, title = {Why does it work?}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2020}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/paper.shtml#converg}, } @InCollection{CBcount, author = {P. Cvitanovi{\'c}}, title = {Counting}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2020}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/paper.shtml#count}, } @TechReport{CBcourse1, author = {P. Cvitanovi{\'c}}, title = {{Nonlinear dynamics 1: Geometry of chaos}}, institution = {Georgia Inst. of Technology}, year = {2016}, address = {Atlanta}, publisher = {Center for Nonlinear Science}, url = {http://ChaosBook.org/course1/about.html}, } @TechReport{CBcourse2, author = {P. Cvitanovi{\'c}}, title = {{Nonlinear dynamics 2: Chaos rules}}, institution = {Georgia Inst. of Technology}, year = {2016}, address = {Atlanta}, publisher = {Center for Nonlinear Science}, url = {http://chaosbook.org/course1/Syllabus2.html}, } @InCollection{CBdiffusion, author = {R. Artuso and P. Cvitanovi{\'c}}, title = {Deterministic diffusion}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2020}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/paper.shtml#diffusion}, } @Article{CBeck91, author = {C. Beck}, title = {Higher correlation functions of chaotic dynamical systems - a graph theoretical approach}, journal = {Nonlinearity}, year = {1991}, volume = {4}, pages = {1131}, doi = {10.1088/0951-7715/4/4/006}, } @Book{CBG16, Title = {{The Symmetries of Things}}, Author = {Conway, J. H. and Burgiel, H. and Goodman-Strauss, C.}, Publisher = {CRC Press}, Year = {2016}, Address = {Boca Raton, FL}, ISBN = {9781439864890} } @InCollection{CBmeasure, author = {P. Cvitanovi\'{c} and R. Artuso and L. Rondoni and E. A. Spiegel}, title = {Transporting densities}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2020}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/paper.shtml#measure}, } @InCollection{CBook:appendHist, author = {R. Mainieri and P. Cvitanovi{\'c}}, title = {A brief history of chaos}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2020}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/paper.shtml#appendHist}, } @InCollection{CBdet, author = {P. Cvitanovi{\'c}}, title = {Spectral determinants}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2020}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/paper.shtml#det}, } @Article{CC92, Title = {Periodic orbit quantization of the anisotropic {Kepler} problem}, Author = {F. Christiansen and P. Cvitanovi{\'c}}, Journal = {Chaos}, Year = {1992}, Pages = {61--69}, Volume = {2}, DOI = {10.1063/1.165899} } @Article{CCR, Title = {The spectrum of the period-doubling operator in terms of cycles}, Author = {F. Christiansen and P. Cvitanovi{\'c} and H. H. Rugh}, Journal = {J. Phys. A}, Year = {1990}, Pages = {L713S--L717S}, Volume = {23}, DOI = {10.1088/0305-4470/23/14/005} } @Article{CCW05, author = {G. Csordas and M. Charalambides and F. Waleffe}, title = {A new property of a class of {Jacobi} polynomials}, journal = {Proc. Amer. Math. Soc.}, year = {2005}, volume = {133}, pages = {3551--3560}, url = {http://www.jstor.org/stable/4097497}, } @Article{CE89, Title = {Periodic orbit quantization of chaotic systems}, Author = {Cvitanovi{\'c}, P. and Eckhardt, B.}, Journal = {Phys. Rev. Lett.}, Year = {1989}, Pages = {823--826}, Volume = {63}, DOI = {10.1103/PhysRevLett.63.823} } @Article{CEEks93, author = {P. Collet and J. -P. Eckmann and H. Epstein and J. Stubbe}, title = {Analyticity for the {Kuramoto-Sivashinsky} equation}, journal = {Physica D}, year = {1993}, volume = {67}, pages = {321--326}, doi = {10.1016/0167-2789(93)90168-z}, } @Article{CEEksgl93, author = {P. Collet and J. -P. Eckmann and H. Epstein and J. Stubbe}, title = {A global attracting set for the {Kuramoto-Sivashinsky} equation}, journal = {Commun. Math. Phys.}, year = {1993}, volume = {152}, pages = {203--214}, doi = {10.1007/978-0-8176-4927-2} } @Article{CeGrNaVi92, author = {E. Celeghini and E. Graziano and K. Nakamura and G. Vitiello}, journal = {Phys. Lett. B}, title = {Finite temperature quantum field theory and gauge field}, year = {1992}, pages = {98--102}, volume = {285}, doi = {10.1016/0370-2693(92)91306-T}, } @Article{CeGrNaVi93, author = {E. Celeghini and E. Graziano and K. Nakamura and G. Vitiello}, journal = {Phys. Lett. B}, title = {Dissipative and inhomogeneous systems and the gauge field}, year = {1993}, pages = {121--126}, volume = {304}, doi = {10.1016/0370-2693(93)91410-O}, } @Book{cellwolf, title = {{Cellular Automata and Complexity: Collected Papers}}, publisher = {Westview Press}, year = {1994}, author = {S. Wolfram}, isbn = {0201626640}, address = {Boulder, CO}, doi = {10.5860/choice.32-2182}, } @Misc{CeMa10, author = {Cerrada, L. and Martin, J. S.}, title = {Matricial representation of period doubling cascade}, year = {2010}, url = {https://arXiv.org/abs/1001.3120}, } @InCollection{CERRS, author = {B. Eckhardt and G. Russberg and P. Cvitanovi{\'c} and P. E. Rosenqvist and P. Scherer}, booktitle = {{Quantum Chaos: Between Order and Disorder}}, publisher = {Cambridge Univ. Press}, title = {Pinball scattering}, year = {1995}, address = {Cambridge UK}, editor = {G. Casati and B. Chirikov}, doi = {10.1017/cbo9780511599989}, url = {http://chaosbook.org/~predrag/papers/preprints.html#CERRS}, } @Article{CFGT15, Title = {Noose structure and bifurcations of periodic orbits in reversible three-dimensional piecewise linear differential systems}, Author = {Carmona, V. and Fern{\'a}ndez-S{\'a}nchez, F. and Garc{\'i}a-Medina, E. and Teruel, A. E.}, Journal = {J. Nonlin. Sci}, Year = {2015}, Pages = {1209--1224}, Volume = {25}, DOI = {10.1007/s00332-015-9251-z} } @Article{CFTsketch, Title = {{Chaotic Field Theory}: {A} sketch}, Author = {Cvitanovi{\'c}, P.}, Journal = {Physica A}, Year = {2000}, Pages = {61--80}, Volume = {288}, DOI = {10.1016/S0378-4371(00)00415-5} } @Article{CG13, Title = {{Lyapunov} analysis: from dynamical systems theory to applications}, Author = {M. Cencini and F. Ginelli}, Journal = {J. Phys. A}, Year = {2013}, Pages = {250301}, Volume = {46}, DOI = {10.1088/1751-8113/46/25/250301} } @Book{CGdynamo, title = {{Stretch, Twist, Fold: the Fast Dynamo}}, publisher = {Springer}, year = {1995}, author = {Gilbert, A. D. and Childress, S.}, isbn = {978-3-662-14014-7}, address = {Berlin}, doi = {10.1007/978-3-540-44778-8}, } @Article{CGM08, Title = {Non-sequential recursive pair substitutions and numerical entropy estimates in symbolic dynamical systems}, Author = {L. M. Calcagnile and S. Galatolo and G. Menconi}, Journal = {J. Nonlin. Sci.}, Year = {2010}, Pages = {723--745}, Volume = {20}, DOI = {10.1007/s00332-010-9071-0} } @Incollection{CGMS02, Title = {Simple choreographic motions of {$N$}-bodies: {A} preliminary study}, Author = {A. Chenciner and J. Gerver and R. Montgomery and C. Sim\'o}, Booktitle = {Geometry, Mechanics and Dynamics}, Publisher = {Springer}, Year = {2002}, Address = {New York}, Editor = {P. Newton and P. Holmes and A. Weinstein}, Pages = {287--308}, DOI = {10.1007/0-387-21791-6_9}, ISBN = {978-0-387-95518-6} } @Article{cgole92, author = {C. Gol{\'e}}, title = {A new proof of the {Aubry-Mather's} theorem}, journal = {Math. Z.}, year = {1992}, volume = {210}, pages = {441--448}, doi = {10.1007/BF02571806}, } @Article{CGS92, Title = {Investigation of the {Lorentz} gas in terms of periodic orbits}, Author = {Cvitanovi{\'c}, P. and Gaspard, P. and Schreiber, T.}, Journal = {Chaos}, Year = {1992}, Pages = {85--90}, Volume = {2}, DOI = {10.1063/1.165902} } @Article{CGV, Title = {On the mode-locking universality for critical circle maps}, Author = {Cvitanovi{\'c}, P. and Gunaratne, G. H. and Vinson, M. J.}, Journal = {Nonlinearity}, Year = {1990}, Pages = {873--885}, Volume = {3}, DOI = {10.1088/0951-7715/3/3/015} } @Article{Cha74, author = {Chazarain, J.}, title = {Formule de {Poisson} pour les vari\'et\'es riemanniennes}, journal = {Inv. Math.}, year = {1974}, volume = {24}, pages = {65--82}, doi = {10.1007/BF01418788}, } @Article{Chairungsee2012109, author = {Chairungsee, S. and Crochemore, M.}, journal = {Theor. Comput. Sci.}, title = {Using minimal absent words to build phylogeny}, year = {2012}, pages = {109--116}, volume = {450}, doi = {10.1016/j.tcs.2012.04.031}, } @Article{ChaKer12, author = {Chandler, G. J. and Kerswell, R. R.}, title = {Invariant recurrent solutions embedded in a turbulent two-dimensional {Kolmogorov} flow}, journal = {J. Fluid Mech.}, year = {2013}, volume = {722}, pages = {554--595}, doi = {10.1017/jfm.2013.122}, } @Article{chand03tf, author = {C. Chandre and S. Wiggins and T. Uzer}, title = {Time-frequency analysis of chaotic systems}, journal = {Physica D}, year = {2003}, volume = {181}, pages = {171--196}, doi = {10.1016/s0167-2789(03)00117-9}, } @Article{Chandr43, Title = {Stochastic problems in physics and astronomy}, Author = {S. Chandrasekhar}, Journal = {Rev. Mod. Phys.}, Year = {1943}, Pages = {1--89}, Volume = {15}, DOI = {10.1103/RevModPhys.15.1} } @Article{chang94, author = {H.-C. Chang}, title = {Wave evolution on a falling film}, journal = {Ann. Rev. Fluid Mech.}, year = {1994}, volume = {26}, pages = {103--136}, doi = {10.1146/annurev.fl.26.010194.000535}, } @Article{ChAnPi85, author = {Chavoya-Aceves, O. and Angulo-Brown, F. and Pi{\~n}a, E.}, journal = {Physica D}, title = {Symbolic dynamics of the cubic map}, year = {1985}, pages = {374--386}, volume = {14}, doi = {10.1016/0167-2789(85)90096-X}, } @Article{CHAOS92, Title = {Periodic orbit theory in classical and quantum mechanics}, Author = {Cvitanovi{\'c}, P.}, Journal = {Chaos}, Year = {1992}, Pages = {1--4}, Volume = {2}, DOI = {10.1063/1.165921} } @Book{ChaosBook, title = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2019}, author = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/}, } @Article{chate94, Title = {Spatiotemporal intermittency regimes of the one-dimensional complex {Ginzburg-Landau} equation}, Author = {H. Chat{\'e}}, Journal = {Nonlinearity}, Year = {1994}, Pages = {185--204}, Volume = {7}, DOI = {10.1088/0951-7715/7/1/007} } @Article{ChaWri81, author = {Chang, S.-J. and Wright, J.}, title = {Transitions and distribution functions for chaotic systems}, journal = {Phys. Rev. A}, year = {1981}, volume = {23}, pages = {1419--1433}, doi = {10.1103/PhysRevA.23.1419}, } @Article{CheLou97, author = {Chen, W. Y. C. and Louck, J. D.}, journal = {Adv. Appl. Math.}, title = {Necklaces, {MSS} sequences, and {DNA} sequences}, year = {1997}, pages = {18--32}, volume = {18}, doi = {10.1006/aama.1996.0494}, } @Article{chemillier04, Title = {Periodic musical sequences and {Lyndon} words}, Author = {Chemillier, M.}, Journal = {Soft Comput.}, Year = {2004}, Pages = {611--616}, Volume = {8}, DOI = {10.1007/s00500-004-0387-2} } @Article{CheMon00, Title = {A remarkable solution of the 3\mbox{-}{b}ody problem in the case of equal masses}, Author = {A. Chenciner and R. Montgomery}, Journal = {Ann. Math.}, Year = {2000}, Pages = {881--901}, Volume = {152}, URL = {http://www.emis.ams.org/journals/Annals/152_3/chencine.pdf} } @Article{chen63, author = {T. Chen}, title = {Equivalence and decomposition of vector fields about an elementary critical point}, journal = {Amer. J. Math.}, year = {1963}, volume = {85}, doi = {10.2307/2373115}, } @Article{Chen90b, Title = {Resonances and transport in the sawtooth map}, Author = {Q. Chen and I. Dana and Meiss, J. D. and N. W. Murray and I. C. Percival}, Journal = {Physica D}, Year = {1990}, Pages = {217--240}, Volume = {46}, DOI = {10.1016/0167-2789(90)90037-P} } @InProceedings{Chenc03, author = {A. Chenciner}, booktitle = {{Proc. ICMP03}}, title = {Symmetries and `simple' solutions of the classical {$N$}-body problem}, year = {2003}, doi = {10.1142/9789812704016_0002}, } @Article{Chenc05, Title = {A note by {P}oincar{\'e}}, Author = {A. Chenciner}, Journal = {Regul. Chaotic Dyn.}, Year = {2005}, Pages = {119--128}, Volume = {10}, URL = {http://www.turpion.org/php/paper.phtml?journal_id=rd&paper_id=306} } @Article{Chernov91, Title = {The ergodicity of a {Hamiltonian} system of two particles in an external field}, Author = {N. I. Chernov}, Journal = {Physica D}, Year = {1991}, Pages = {233--239}, Volume = {53}, DOI = {10.1016/0167-2789(91)90063-F} } @Article{Chernov97, Title = {Entropy, {Lyapunov} exponents, and mean free path for billiards}, Author = {Chernov, N.}, Journal = {J. Stat. Phys.}, Year = {1997}, Pages = {1--29}, Volume = {88}, DOI = {10.1007/BF02508462} } @Article{Cherry25, author = {Cherry, T. M.}, journal = {Trans. Camb. Phil. Soc.}, title = {Some examples of trajectories defined by differential equations of a generalised dynamical type}, year = {1925}, pages = {169--200}, volume = {23}, } @Article{CheSu90, author = {Cheng, C. Q. and Sun, Y. S.}, title = {Existence of invariant tori in three-dimensional measure-preserving mappings}, journal = {Celestial Mech. Dynam. Astronom.}, year = {1989}, volume = {47}, pages = {275--292}, doi = {10.1007/BF00053456} } @Article{ChGu99, author = {W. G. Choe and J. Guckenheimer}, title = {Computing periodic orbits with high accuracy}, journal = {Computer Meth. Appl. Mech. and Engin.}, year = {1999}, volume = {170}, pages = {331--341}, doi = {10.1016/S0045-7825(98)00201-1} } @Article{CHHM98, author = {Cendra, H. and Holm, D. D. and Hoyle, M. J. W. and Marsden, J. E.}, title = {The {Maxwell-Vlasov} equations in {Euler-Poincar{\'e}} form}, journal = {J. Math. Phys.}, year = {1998}, volume = {39}, pages = {3138--3157}, doi = {10.1063/1.532244}, } @Book{Chicone2006, title = {{Ordinary Differential Equations with Applications}}, publisher = {Springer}, year = {2006}, author = {C. Chicone}, address = {New York}, doi = {10.1007/0-387-35794-7}, } @Article{Chirikov79, Title = {A universal instability of many-dimensional oscillator system}, Author = {B. V. Chirikov}, Journal = {Phys. Rep.}, Year = {1979}, Pages = {263--379}, Volume = {52}, DOI = {10.1016/0370-1573(79)90023-1} } @Article{ChMePe87, Title = {Orbit extension method for finding unstable orbits}, Author = {Q. Chen and J.D. Meiss and I.C. Percival}, Journal = {Physica D}, Year = {1987}, Pages = {143--154}, Volume = {29}, DOI = {10.1016/0167-2789(87)90051-0} } @Article{Chomsky1956, Title = {Three models for the description of language}, Author = {Chomsky, N.}, Journal = {IRE Trans. on Information Theory}, Year = {1956}, Pages = {113--124}, Volume = {2}, DOI = {10.1109/TIT.1956.1056813} } @Incollection{ChomskySchutzenberger1963, author = {Chomsky, N. and Sch\"utzenberger, M. P.}, title = {The algebraic theory of context-free languages}, booktitle = {{Computer Programming and Formal Systems}}, publisher = {Elsevier}, year = {1963}, editor = {P. Braffort and D. Hirschberg}, isbn = {9780080957555}, pages = {118--161}, address = {Amsterdam}, doi = {10.1016/S0049-237X(08)72023-8}, } @Article{Choss02, author = {P. Chossat}, journal = {Acta Appl. Math.}, title = {The reduction of equivariant dynamics to the orbit space for compact group actions}, year = {2002}, pages = {71--94}, volume = {70}, doi = {10.1023/A:1013970014204}, } @Article{Choss93, Title = {Forced reflectional symmetry breaking of an {O(2)}-symmetric homoclinic tangle}, Author = {Chossat, P.}, Journal = {Nonlinearity}, Year = {1993}, Pages = {723--731}, Volume = {6}, DOI = {10.1088/0951-7715/6/5/003} } @Book{Chossat94, author = {P. Chossat and G. Iooss}, publisher = {Springer}, title = {{The {Taylor-Couette} Problem}}, year = {1994}, address = {New York}, doi = {10.1007/978-1-4612-4300-7}, } @Book{ChossLaut00, title = {{Methods in Equivariant Bifurcations and Dynamical Systems}}, publisher = {World Scientific}, year = {2000}, author = {P. Chossat and R. Lauterbach}, isbn = {978-981-02-3828-5}, address = {Singapore}, doi = {10.1142/4062}, } @Article{ChPaRu90, Title = {Determination of correlation spectra in chaotic systems}, Author = {Christiansen, F. and Paladin, G. and Rugh, H. H.}, Journal = {Phys. Rev. Lett.}, Year = {1990}, Pages = {2087--2090}, Volume = {65}, DOI = {10.1103/PhysRevLett.65.2087} } @Book{ChPiWa89, Title = {{Group Representation Theory for Physicists}}, Author = {Chen, J.-Q. and Ping, J. and Wang, F.}, Publisher = {World Scientific}, Year = {1989}, Address = {Singapore}, DOI = {10.1142/0262} } @Article{ChriPol96, Title = {Symbolic encoding in symplectic maps}, Author = {Christiansen, F. and Politi, A.}, Journal = {Nonlinearity}, Year = {1996}, Pages = {1623--1640}, Volume = {9}, DOI = {10.1088/0951-7715/9/6/014} } @Article{ChriPol97, Title = {Guidelines for the construction of a generating partition in the standard map}, Author = {Christiansen, F. and Politi, A.}, Journal = {Physica D}, Year = {1997}, Pages = {32--41}, Volume = {109}, DOI = {10.1016/S0167-2789(97)00156-5} } @Article{Christiansen97, Title = {Hopf's last hope: {Spatiotempora}l chaos in terms of unstable recurrent patterns}, Author = {F. Christiansen and P. Cvitanovi{\'c} and V. Putkaradze}, Journal = {Nonlinearity}, Year = {1997}, Pages = {55--70}, Volume = {10}, DOI = {10.1088/0951-7715/10/1/004} } @Article{ChrLueOtt11, Title = {Stretching and folding versus cutting and shuffling: {An} illustrated perspective on mixing and deformations of continua}, Author = {{Christov}, I. C. and {Lueptow}, R. M. and {Ottino}, J. M.}, Journal = {Amer. J. Phys.}, Year = {2011}, Pages = {359--367}, Volume = {79}, DOI = {10.1119/1.3533213} } @Article{ChrPol95, Title = {Generating partition for the standard map}, Author = {Christiansen, F. and Politi, A.}, Journal = {Phys. Rev. E}, Year = {1995}, Pages = {R3811--R3814}, Volume = {51}, DOI = {10.1103/PhysRevE.51.R3811} } @Article{ChRu97, Title = {Computing {Lyapunov} spectra with continuous {Gram-Schmidt} orthonormalization}, Author = {Christiansen, F. and Rugh, H. H.}, Journal = {Nonlinearity}, Year = {1997}, Pages = {1063--1072}, Volume = {10}, DOI = {10.1088/0951-7715/10/5/004} } @Article{ChSc, Title = {Symplectic integration of {Hamiltonian} systems}, Author = {P. J. Channell and C. Scovel}, Journal = {Nonlinearity}, Year = {1990}, Pages = {231--259}, Volume = {3}, DOI = {10.1088/0951-7715/3/2/001} } @Article{cima_algebraic_1997, author = {A. Cima}, title = {Algebraic properties of the {Lyapunov} and period constants}, journal = {Rocky Mountain J. Math.}, year = {1997}, volume = {27}, pages = {471--502}, doi = {10.1216/rmjm/1181071923}, } @Article{cima_dynamics_2006, author = {A. Cima}, title = {Dynamics of some rational discrete dynamical systems via invariants}, journal = {Int. J. Bifur. Chaos}, year = {2006}, volume = {16}, pages = {631--646}, doi = {10.1142/s0218127406015027}, } @Article{cima_number_2008, author = {A. Cima}, title = {On the number of critical periods for planar polynomial systems}, journal = {Nonlinear Anal.}, year = {2008}, volume = {69}, pages = {1889--1903}, doi = {10.1016/j.na.2007.07.031}, } @Article{cima_periodic_2007, author = {A. Cima and A. Gasull and F. Manosas}, title = {Periodic orbits in complex {Abel} equations}, journal = {J. Diff. Eqn.}, year = {2007}, volume = {232}, pages = {314--328}, doi = {10.1016/j.jde.2006.09.002}, } @Article{cima_relation_1998, author = {A. Cima}, title = {On the relation between index and multiplicity}, journal = {J. London Math. Soc.}, year = {1998}, volume = {57}, pages = {757--768}, doi = {10.1112/s0024610798006188}, } @Article{cima_studying_2008, author = {A. Cima and A. Gasull and V. Manosa}, title = {Studying discrete dynamical systems through differential equations}, journal = {J. Diff. Eqn.}, year = {2008}, volume = {244}, pages = {630--648}, doi = {10.1016/j.jde.2007.10.013}, } @Article{CIPR90, author = {F. Christiansen and S. Isola and G. Paladin and H. H. Rugh}, title = {Mixing rates and exterior forms in chaotic systems}, journal = {J. Phys. A}, year = {1990}, volume = {23}, pages = {L1301--L1308}, doi = {10.1088/0305-4470/23/24/004}, } @Misc{CK, author = {Kaufmann and P. Cvitanovi{\'c} and in preparation.}, } @Article{CK97, author = {O. Cepas and J. Kurchan}, title = {Canonically invariant formulation of {Langevin} and {Fokker-Planck} equations}, journal = {Eur. Phys. J. B}, year = {1998}, volume = {2}, pages = {221--223}, doi = {10.1007/s100510050243}, } @Article{Cleveland, Title = {Energy dissipation in tapping-mode atomic force microscopy}, Author = {J. P. Cleveland and B. Anczykowski and A. E. Schmid and V. B. Elings}, Journal = {Appl. Phys. Lett.}, Year = {1998}, Pages = {2613}, Volume = {72}, DOI = {10.1063/1.121434} } @Article{cm, Title = {Statistical characterization of periodic, area-preserving mappings}, Author = {J. R. Cary and J. D. Meiss and A. Bhattacharjee}, Journal = {Phys. Rev. A}, Year = {1981}, Pages = {2744--2746}, Volume = {23}, DOI = {10.1103/PhysRevA.23.2744} } @Article{CM87tran, author = {H. Chat{\'e} and Manneville, P.}, journal = {Phys. Rev. Lett.}, title = {Transition to turbulence via spatiotemporal intermittency}, year = {1987}, pages = {112}, volume = {58}, doi = {10.1007/978-3-642-74554-6_75}, } @Article{CMRSY10, Title = {Amplitude-phase synchronization at the onset of permanent spatiotemporal chaos}, Author = {Chian, A. C. and Miranda, R. A. and Rempel, E. L. and Saiki, Y. and Yamada, M.}, Journal = {Phys. Rev. Lett.}, Year = {2010}, Pages = {254102}, Volume = {104}, DOI = {10.1103/PhysRevLett.104.254102} } @Misc{CNS, title = {{Center for Nonlinear Science}}, address = {Georgia Inst. of Technology}, url = {http://www.cns.gatech.edu}, } @Article{cohen72, author = {B. I. Cohen and J. A. Krommes and W. M. Tang and M. N. Rosenbluth}, title = {Non-linear saturation of the dissipative trapped-ion mode by mode coupling}, journal = {Nucl. Fusion}, year = {1972}, volume = {16}, pages = {971--991}, doi = {10.1088/0029-5515/16/6/009}, } @Article{CoIs, author = {P. Collet and S. Isola}, title = {Essential spectrum of the transfer operator for expanding {Markov} maps}, journal = {Commun. Math. Phys.}, year = {1991}, volume = {139}, pages = {551--557}, doi = {10.1007/BF02101879}, } @Article{CoKoPa94, Title = {Shadowing orbits of ordinary differential equations}, Author = {B. A. Coomes and H. Ko\c{c}ak and K. J. Palmer}, Journal = {J. Comput. Appl. Math.}, Year = {1994}, Pages = {35--43}, Volume = {52}, DOI = {10.1016/0377-0427(94)90347-6} } @Article{CoKoPa97, Title = {Long periodic shadowing}, Author = {B. A. Coomes and H. Ko\c{c}ak and K. J. Palmer}, Journal = {Numer. Algorithms}, Year = {1997}, Pages = {55--78}, Volume = {14}, DOI = {10.1023/A:1019148510433} } @Article{Col97, author = {A. J. Coleman}, title = {Groups and physics -- {Dogmatic} opinions of a senior citizen}, journal = {Notices Amer. Math. Soc.}, year = {1997}, volume = {44}, pages = {8--17}, url = {http://www.ams.org/notices/199701/coleman.pdf}, } @Article{Colaneri05, author = {P. Colaneri}, journal = {Annual Rev. Control}, title = {Theoretical aspects of continuous-time periodic systems}, year = {2005}, pages = {205--215}, volume = {29}, doi = {10.1016/j.arcontrol.2005.04.001}, } @Article{CoLe84, author = {P. Collet and Y. Levy}, title = {Ergodic properties of the {Lozi} mappings}, journal = {Commun. Math. Phys.}, year = {1984}, volume = {93}, pages = {461}, doi = {10.1007/978-0-387-21830-4_14}, } @Book{CoLiSh96, title = {{Ideals, Varieties and Algorithms}}, publisher = {Springer}, year = {2007}, author = {D. A. Cox and J. B. Little and D. 0'Shea}, address = {New York}, doi = {10.1007/978-0-387-35651-8}, } @Article{collet80, author = {P. Collet and J.-P. Eckmann and O. E. Lanford}, title = {Universal properties of maps on an interval}, journal = {Commun. Math. Phys.}, year = {1980}, volume = {76}, pages = {211--254S}, doi = {10.1007/BF02193555} } @Article{Collinson62, Title = {A class of conserved tensors in an arbitrary gravitational field}, Author = {Collinson, C. D.}, Journal = {Math. Proc. Cambridge Philos. Soc.}, Year = {1962}, Pages = {346--362}, Volume = {58}, DOI = {10.1017/S0305004100036550} } @Article{condisfam1, Title = {Localized oscillations in conservative or dissipative networks of weakly coupled autonomous oscillators}, Author = {J.-A. Sepulchre and R. S. MacKay}, Journal = {Nonlinearity}, Year = {1997}, Pages = {679--713}, Volume = {10}, DOI = {10.1088/0951-7715/10/3/006} } @Article{conjug_Fred, author = {P. Cvitanovi{\'c} and C. P. Dettmann and R. Mainieri and G. Vattay}, title = {Trace formulae for stochastic evolution operators: {Smooth} conjugation method}, journal = {Nonlinearity}, year = {1999}, volume = {12}, pages = {939}, doi = {10.1088/0951-7715/12/4/312}, } @Article{const85, author = {Constantin, P. and Foias, C. and Manley, O. P. and T{\'e}mam, R.}, title = {Determining modes and fractal dimension of turbulent flows}, journal = {J. Fluid Mech.}, year = {1985}, volume = {150}, pages = {427--440}, doi = {10.1017/S0022112085000209}, } @Book{constantin_integral_1989, title = {{Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations}}, publisher = {Springer}, year = {1989}, author = {P. Constantin and C. Foias and B. Nicolaenko and R. T{\'e}mam}, address = {New York}, doi = {10.1007/978-1-4612-3506-4}, } @Article{Constantin97, Title = {The elusive singularity}, Author = {P. Constantin}, Journal = {Proc. Natl. Acad. Sci. USA}, Year = {1997}, Pages = {12761}, Volume = {94}, DOI = {10.1073/pnas.94.24.12761} } @Book{contebook, title = {{The {Painlev{\'e}} Property: One Century Later}}, publisher = {Springer}, year = {1999}, author = {R. Conte}, address = {New York}, } @Book{Cornwell97, title = {{Group Theory in Physics: An Introduction}}, publisher = {Academic}, year = {1997}, author = {Cornwell, J. F.}, address = {New York}, isbn = {9780121898007}, } @Book{Cotton08, author = {Cotton, F. A.}, publisher = {Wiley}, title = {{Chemical Applications of Group Theory}}, year = {2008}, address = {New York}, edition = {3}, isbn = {978-0-471-51094-9}, } @Article{CouTre78, author = {P. Coullet and C. Tresser}, title = {It{\'e}rations d'endomorphismes et groupe de renormalisation}, journal = {J. Phys. Colloques C5}, year = {1978}, volume = {39}, pages = {25--28}, doi = {10.1051/jphyscol:1978513}, } @Article{CouTre78a, author = {Coullet, P. and Tresser, C.}, title = {Iterations of endomorphisms and renormalization group}, journal = {C. R. Acad. Sc. Paris A}, year = {1978}, volume = {287}, pages = {577--581}, url = {http://gallica.bnf.fr/ark:/12148/bpt6k6238948x/f107.image.r=Tresser%20Coullet%20Hebdomadaires%201978?rk=21459;2} } @Book{CoVanLo88, title = {{Handbook for Matrix Computations}}, publisher = {SIAM}, year = {1988}, author = {Coleman, T. F. and Van Loan, C.}, address = {Philadelphia}, doi = {10.1137/1.9781611971040}, } @Article{cox02jcomp, author = {S. M. Cox and P. C. Matthews}, title = {Exponential time differencing for stiff systems}, journal = {J. Comp. Phys.}, year = {2002}, volume = {176}, pages = {430--455}, doi = {10.1006/jcph.2002.6995}, } @Book{Coxeter12, title = {{Regular Polytopes}}, publisher = {Dover}, year = {1948}, author = {H. S. M. Coxeter}, address = {New York}, isbn = {9780486141589}, } @Article{Coxeter34, author = {H. S. M. Coxeter}, journal = {Ann. Math.}, title = {Discrete groups generated by reflections}, year = {1934}, pages = {588--621}, volume = {35}, doi = {10.2307/1968753}, } @Article{Coxeter35, Title = {The complete enumeration of finite groups of the form {$ R_i^2 = (R_i R_j)^{k_{ij}}=1$}}, Author = {Coxeter, H. S. M.}, Journal = {J. London Math. Soc.}, Year = {1935}, Pages = {21--25}, Volume = {s1--10}, DOI = {10.1112/jlms/s1-10.37.21} } @Book{Coxeter89, author = {Coxeter, H. S. M.}, publisher = {Wiley}, title = {{Introduction to Geometry}}, year = {1989}, address = {New York}, edition = {2}, isbn = {978-0-471-50458-0}, } @Article{cpmani, author = {A. J. Homburg and H. M. Osinga and G. Vegter}, title = {On the computation of invariant manifolds of fixed points}, journal = {Z. Angew. Math. Phys.}, year = {1995}, volume = {46}, pages = {171}, doi = {10.1007/bf00944751}, } @Article{CPR75, Title = {Isolated unstable periodic orbits}, Author = {R. C Churchill and G. Pecelli and D. L Rod}, Journal = {J. Diff. Eqn.}, Year = {1975}, Pages = {329--348}, Volume = {17}, DOI = {10.1016/0022-0396(75)90047-9} } @Incollection{CPR79, Title = {A survey of the {H{\'e}non-Heiles Hamiltonian} with applications to related examples}, Author = {Churchill, R. C. and Pecelli, G. and Rod, D. L.}, Booktitle = {Stochastic Behavior in Classical and Quantum {Hamiltonian} Systems}, Publisher = {Springer}, Year = {1979}, Address = {Berlin}, Editor = {Casati, G. and Ford, J.}, Pages = {76--136}, DOI = {10.1007/BFb0021739}, ISBN = {978-3-540-09120-2} } @Article{CPR80, Title = {Stability transitions for periodic orbits in {Hamiltonian} systems}, Author = {R. C Churchill and G. Pecelli and D. L Rod}, Journal = {Arch. Rational Mech. Anal.}, Year = {1980}, Pages = {329--348}, Volume = {73}, DOI = {10.1016/0022-0396(75)90047-9} } @Article{crawford89, author = {J. D. Crawford and P. D. Hislop}, title = {Application of the method of spectral deformation to the {Vlasov-Poisson} system}, journal = {Ann. Phys.}, year = {1989}, volume = {189}, pages = {265--317}, doi = {10.1016/0003-4916(89)90166-8}, } @Article{crawford97, author = {J. D. Crawford}, title = {Amplitude equations for electrostatic waves: {Universal} singular behavior in the limit of weak instability}, journal = {Phys. Plasmas}, year = {1995}, volume = {2}, pages = {97--128}, doi = {10.1063/1.871120}, } @Article{CrCa, author = {J. D. Crawford and J. R. Cary}, title = {Decay of correlations in a chaotic measure preserving transformation}, journal = {Physica D}, year = {1983}, volume = {6}, pages = {223--232}, doi = {10.1016/0167-2789(83)90007-6}, } @Article{Creagh91, author = {S. C. Creagh and R. G. Littlejohn}, title = {Semiclassical trace formulas in the presence of continuous symmetries}, journal = {Phys. Rev. A}, year = {1991}, volume = {44}, pages = {836--850}, doi = {10.1103/physreva.44.836}, numpages = {14}, } @Article{Creagh92, author = {S. C. Creagh and R. G. Littlejohn}, title = {Semiclassical trace formulas for systems with {non-Abelian} symmetry}, journal = {J. Phys. A}, year = {1992}, volume = {25}, pages = {1643--1669}, doi = {10.1088/0305-4470/25/6/021}, } @Article{Creagh93, author = {S C Creagh}, title = {Semiclassical mechanics of symmetry reduction}, journal = {J. Phys. A}, year = {1993}, volume = {26}, pages = {95--118}, doi = {10.1088/0305-4470/26/1/013}, } @Article{Creagh94, Title = {Quantum zeta function for perturbed cat maps}, Author = {S. C. Creagh}, Journal = {Chaos}, Year = {1995}, Pages = {477--493}, Volume = {5}, DOI = {10.1063/1.166119} } @Article{CriKnDeEsp12, Title = {Follow the fugitive: an application of the method of images to open systems}, Author = {Cristadoro, G. and Knight, G. and Degli Esposti, M.}, Journal = {J. Phys. A}, Year = {2013}, Pages = {272001}, Volume = {46}, DOI = {10.1088/1751-8113/46/27/272001} } @Article{Cristad06, Title = {Fractal diffusion coefficient from dynamical zeta functions}, Author = {G. Cristadoro}, Journal = {J. Phys. A}, Year = {2006}, Pages = {L151}, Volume = {39}, DOI = {10.1088/0305-4470/39/10/L01} } @Article{CRMRF02, author = {A. {C.-L.} Chian and E. L. Rempel and E. E. Macau and R. R. Rosa and F. Christiansen}, title = {High-dimensional interior crisis in the {Kuramoto-Sivashinsky} equation}, journal = {Phys. Rev. E}, year = {2002}, volume = {65}, pages = {035203}, doi = {10.1103/physreve.65.035203}, } @Book{CRob94, title = {{Dynamical Systems: Stability, Symbolic Dynamics, and Chaos}}, publisher = {CRC Press}, year = {1995}, author = {Robinson, C.}, address = {Boca Raton FL}, isbn = {9780849384950}, } @Article{CroDav06, Title = {Efficient detection of periodic orbits in chaotic systems by stabilizing transformations}, Author = {J. J. Crofts and R. L. Davidchack}, Journal = {SIAM J. Sci. Comp.}, Year = {2006}, Pages = {1275--1288}, Volume = {28}, DOI = {10.1137/050623401} } @Article{CroDav09, Title = {On the use of stabilizing transformations for detecting unstable periodic orbits in high-dimensional flows}, Author = {J. J. Crofts and R. L. Davidchack}, Journal = {Chaos}, Year = {2009}, Pages = {033138}, Volume = {19}, DOI = {10.1063/1.3222860} } @PhdThesis{Crofts07thesis, author = {J. J. Crofts}, title = {{Efficient Method for Detection of Periodic Orbits in Chaotic Maps and Flows}}, school = {Univ. of Leicester}, year = {2007}, address = {Leicester, UK}, url = {https://arxiv.org/abs/nlin.CD/0706.1940}, } @Article{cross93, Title = {Pattern formation outside of equilibrium}, Author = {Cross, M. C. and Hohenberg, P. C.}, Journal = {Rev. Mod. Phys.}, Year = {1993}, Pages = {851--1112}, Volume = {65}, DOI = {10.1103/RevModPhys.65.851} } @Article{cross94sp, author = {Cross, M. C. and Hohenberg, P. C.}, title = {Spatiotemporal chaos}, journal = {Science}, year = {1994}, volume = {263}, pages = {1569--1570}, doi = {10.1126/science.263.5153.1569}, } @Article{CS01, Title = {A brief review and a new treatment for rigid bodies collision models}, Author = {E. Cataldo and R. Sampaio}, Journal = {J. Braz. Soc. Mech. Sci.}, Year = {2001}, Pages = {63--78}, Volume = {23}, DOI = {10.1590/S0100-73862001000100006} } @Article{CU-BBM80n, author = {B. B. Mandelbrot}, title = {Fractal aspects of the iteration {$z \to \lambda z(1-z)$} for complex {$\lambda$} and {$z$}}, journal = {Ann. New York Acad. Sci.}, year = {1980}, volume = {357}, pages = {249}, doi = {10.1111/j.1749-6632.1980.tb29690.x}, } @Article{Cucchieri98, Title = {Numerical study of the fundamental modular region in the minimal {Landau} gauge}, Author = {A. Cucchieri}, Journal = {Nucl. Phys. B}, Year = {1998}, Pages = {365--379}, Volume = {521}, DOI = {10.1016/S0550-3213(98)00235-1} } @Article{CunEld07, Title = {The extended { Freudenthal Magic Square} and { Jordan} algebras}, Author = {Cunha, I. and Elduque, A.}, Journal = {Manuscripta Math.}, Year = {2007}, Pages = {325--351}, Volume = {123}, DOI = {10.1007/s00229-007-0099-x} } @Article{Curry78, author = {Curry, J. H.}, title = {A generalized {Lorenz} system}, journal = {Commun. Math. Phys.}, year = {1978}, volume = {60}, pages = {193--204}, doi = {10.1007/bf01612888}, } @Inbook{Curry80, Title = {An algorithm for finding closed orbits}, Author = {Curry, J. H.}, Editor = {Nitecki, Z. and Robinson, C.}, Pages = {111--120}, Publisher = {Springer}, Year = {1980}, Address = {Berlin}, Booktitle = {Global Theory of Dynamical Systems: Proc. Int. Con., Northwestern Univ., June 18--22, 1979}, DOI = {10.1007/BFb0086983} } @Book{CushBat97, title = {{Global Aspects of Classical Integrable Systems}}, publisher = {Birkh{\"{a}}user}, year = {1997}, author = {Cushman, R. H. and Bates, L. M.}, address = {Boston}, doi = {10.1007/978-3-0348-8891-2}, } @Article{CV93, author = {Cvitanovi{\'c}, P. and Vattay, G.}, title = {Entire {Fredholm} determinants for evaluation of semi-classical and thermodynamical spectra}, journal = {Phys. Rev. Lett.}, year = {1993}, volume = {71}, pages = {4138--4141}, doi = {10.1103/PhysRevLett.71.4138}, } @Book{cvetko, title = {{Spectra of Graphs}}, publisher = {Academic}, year = {1980}, author = {D. M. Cvektovi{\'c} and M. Doob and H. Sachs}, address = {New York}, isbn = {9780121951504}, } @Unpublished{Cvi07, Title = {Continuous symmetry reduced trace formulas}, Author = {P. Cvitanovi\'{c}}, Note = {Unpublished}, Year = {2007}, URL = {http://ChaosBook.org/~predrag/papers/Cvi07.pdf} } @InProceedings{Cvi92, Title = {The power of chaos}, Author = {Cvitanovi{\'c}, P.}, Booktitle = {Applications of Chaos}, Year = {1992}, Address = {New York}, Editor = {J. H. Kim and J. Stringer}, Organization = {EPRI workshop}, Publisher = {Wiley}, URL = {http://chaosbook.org/~predrag/papers/preprints.html#epri} } @Article{CviGib10, Title = {Geometry of turbulence in wall-bounded shear flows: {Periodic} orbits}, Author = {Cvitanovi{\'c}, P. and Gibson, J. F.}, Journal = {Phys. Scr. T}, Year = {2010}, Pages = {014007}, Volume = {142}, DOI = {10.1088/0031-8949/2010/T142/014007} } @InProceedings{CviLip12, author = {P. Cvitanovi{\'c} and D. Lippolis}, booktitle = {{Let's Face Chaos through Nonlinear Dynamics}}, title = {Knowing when to stop: {How} noise frees us from determinism}, year = {2012}, address = {Melville, New York}, editor = {M. Robnik and V. G. Romanovski}, pages = {82--126}, publisher = {Am. Inst. of Phys.}, doi = {10.1063/1.4745574}, eprint = {1206.5506}, eprinttype = {arxiv}, } @Article{CviMyr89, Title = {Complex universality}, Author = {Cvitanovi{\'c}, P. and Myrheim, J.}, Journal = {Commun. Math. Phys.}, Year = {1989}, Pages = {225--254}, Volume = {121}, DOI = {10.1007/BF01217804} } @Proceedings{CviPerWirz92, title = {{Quantum Chaos - Quantum Measurement}}, year = {1992}, editor = {Cvitanovi{\'c}, P. and Percival, I. and Wirzba, A.}, series = {NATO Sci. Ser. C}, volume = {358}, doi = {10.1007/978-94-015-7979-7}, } @Article{CviPik93, Title = {Cycle expansion for power spectrum}, Author = {Cvitanovi{\'c}, P. and Pikovsky, A.}, Journal = {Proc. SPIE}, Year = {1993}, Pages = {290--298}, Volume = {2038}, DOI = {10.1117/12.162683} } @Article{CvitaEckardt, Title = {Symmetry decomposition of chaotic dynamics}, Author = {Cvitanovi{\'c}, P. and Eckhardt, B.}, Journal = {Nonlinearity}, Year = {1993}, Pages = {277--311}, Volume = {6}, DOI = {10.1088/0951-7715/6/2/008} } @Article{Cvitanovic1991, Title = {Periodic orbits as the skeleton of classical and quantum chaos}, Author = {P. Cvitanovi{\'c}}, Journal = {Physica D}, Year = {1991}, Pages = {138--151}, Volume = {51}, DOI = {10.1016/0167-2789(91)90227-Z} } @Article{Cvitanovic1995109, Title = {Dynamical averaging in terms of periodic orbits}, Author = {Cvitanovi{\'c}, P.}, Journal = {Physica D}, Year = {1995}, Pages = {109--123}, Volume = {83}, DOI = {10.1016/0167-2789(94)00256-P} } @Inproceedings{CvitLanCrete02, author = {P. Cvitanovi{\'c} and Y. Lan}, title = {Turbulent fields and their recurrences}, booktitle = {{Correlations and Fluctuations in QCD : Proceedings of 10. International Workshop on Multiparticle Production}}, year = {2003}, editor = {N. Antoniou}, isbn = {978-981-238-455-3}, pages = {313--325}, address = {Singapore}, publisher = {World Scientific}, doi = {10.1142/9789812704641_0032}, } @Book{cvt89b, author = {P. Cvitanovi{\'c}}, publisher = {Adam Hilger}, title = {{Universality in Chaos}}, year = {1989}, address = {Bristol}, edition = {2}, doi = {10.1201/9780203734636}, } @InCollection{CVW96, author = {Cvitanovi{\'c}, P. and Vattay, G. and Wirzba, A.}, booktitle = {{Classical, Semiclassical and Quantum Dynamics in Atoms}}, publisher = {Springer}, title = {Quantum fluids and classical determinants}, year = {1997}, address = {New York}, editor = {H. Friedrich and B. Eckhardt}, pages = {29--62}, doi = {10.1007/BFb0105968}, } @Article{D_q, Title = {Generalized dimensions of strange attractors}, Author = {P. Grassberger}, Journal = {Phys. Lett. A}, Year = {1983}, Pages = {227--230}, Volume = {97}, DOI = {10.1016/0375-9601(83)90753-3} } @Article{DaFi85, Title = {Diffusion in the standard map}, Author = {I. Dana and S. Fishman}, Journal = {Physica D}, Year = {1985}, Pages = {63--74}, Volume = {17}, DOI = {10.1016/0167-2789(85)90134-4} } @Article{DaFrTr08, Title = {Algorithms for rigorous entropy bounds and symbolic dynamics}, Author = {S. Day and R. Frongillo and R. Trevi{\~n}o}, Journal = {SIAM J. Appl. Dyn. Syst.}, Year = {2008}, Pages = {1477--1506}, Volume = {7}, DOI = {10.1137/070688080} } @Article{Dahlqv94, Title = {Determination of resonance spectra for bound chaotic systems}, Author = {P. Dahlqvist}, Journal = {J. Phys. A}, Year = {1994}, Pages = {763--785}, Volume = {27}, DOI = {10.1088/0305-4470/27/3/020} } @Article{Dahlqvist95, Title = {Approximate zeta functions for the {Sinai} billiard and related systems}, Author = {P. Dahlqvist}, Journal = {Nonlinearity}, Year = {1995}, Pages = {11}, Volume = {8}, DOI = {10.1088/0951-7715/8/1/002} } @Article{DAlPol90, Title = {Hierarchical approach to complexity with applications to dynamical systems}, Author = {D'Alessandro, G. and Politi, A.}, Journal = {Phys. Rev. Lett.}, Year = {1990}, Pages = {1609--1612}, Volume = {64}, DOI = {10.1103/PhysRevLett.64.1609} } @Article{DaMuPe88, Title = {Resonances and diffusion in periodic {Hamiltonian} maps}, Author = {I. Dana and N. V. Murray and I. C. Percival}, Journal = {Phys. Rev. Lett.}, Year = {1988}, Pages = {233}, Volume = {62}, DOI = {10.1103/PhysRevLett.62.233} } @Article{Dana13, author = {Dana, I.}, title = {Classical and quantum transport in one-dimensional periodically kicked systems}, journal = {Canadian J. Chem.}, year = {2014}, volume = {92}, pages = {77--84}, doi = {10.1139/cjc-2013-0374}, } @Article{dana89, Title = {Hamiltonian transport on unstable periodic orbits}, Author = {I. Dana}, Journal = {Physica D}, Year = {1989}, Pages = {205}, Volume = {39}, DOI = {10.1016/0167-2789(89)90005-5} } @Article{Dana90, Title = {Organization of chaos in area-preserving maps}, Author = {I. Dana}, Journal = {Phys. Rev. Lett.}, Year = {1990}, Pages = {2339}, Volume = {64}, DOI = {10.1103/PhysRevLett.64.2339} } @Article{DanChe04, Title = {Periodic orbits and chaotic-diffusion probability distributions}, Author = {I. Dana and V. E. Chernov}, Journal = {Physica A}, Year = {2004}, Pages = {219--229}, Volume = {332}, DOI = {10.1016/j.physa.2003.10.050} } @Article{Dang86, Title = {Steady-state mode interactions in the presence of {0(2)}-symmetry}, Author = {Dangelmayr, G.}, Journal = {Dyn. Sys.}, Year = {1986}, Pages = {159--185}, Volume = {1}, DOI = {10.1080/02681118608806011} } @Article{DASB11, Title = {Optimal transfers between unstable periodic orbits using invariant manifolds}, Author = {Davis, K. E. and Anderson, R. L. and Scheeres, D. J. and Born, G. H.}, Journal = {Celestial Mech. Dynam. Astronom.}, Year = {2011}, Pages = {241--264}, Volume = {109}, DOI = {10.1007/s10569-010-9327-x} } @Book{DasBuch, title = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2019}, author = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/}, } @InCollection{DasBuchMirror, author = {P. Cvitanovi{\'c}}, title = {World in a mirror}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2020}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/paper.shtml#discrete}, } @Book{DasOkubo14, title = {{Lie Groups and Lie Algebras for Physicists}}, publisher = {World Scientific Publishing Company}, year = {2014}, author = {Das, A. and Okubo, S.}, isbn = {9789814603294}, doi = {10.1142/9169}, } @Misc{Davidchack_priv, author = {R. L. Davidchack}, note = {Private communication}, year = {2007}, } @Book{Davis08, Title = {{The Geometry and Topology of Coxeter Groups}}, Author = {Davis, M. W.}, Publisher = {Princeton Univ. Press}, Year = {2008}, ISBN = {9780691131382} } @Misc{Davis10, Title = {Lectures on orbifolds and reflection groups}, Author = {Davis, M. W.}, Year = {2010}, URL = {http://math.osu.edu/sites/math.osu.edu/files/08-05-MRI-preprint.pdf} } @Article{DavisSIAM08, Title = {Spanning multiple worlds}, Author = {Davis, P. J.}, Journal = {SIAM News}, Year = {2008}, Volume = {41}, URL = {http://www.siam.org/news/news.php?id=1476} } @Article{dawson_collections_1997, author = {S. P. Dawson and A. M. Mancho}, title = {Collections of heteroclinic cycles in the {Kuramoto-Sivashinsky} equation}, journal = {Physica D}, year = {1997}, volume = {100}, pages = {231--256}, doi = {10.1016/s0167-2789(96)00209-6}, } @Article{dCH02, author = {de Carvalho, A. and Hall, T.}, journal = {Nonlinearity}, title = {How to prune a horseshoe}, year = {2002}, pages = {R19--R68}, volume = {15}, doi = {10.1088/0951-7715/15/3/201}, } @Article{DCTSCD14, Title = {Estimating the dimension of the inertial manifold from unstable periodic orbits}, Author = {Ding, X. and Chat\'e, H. and Cvitanovi\'c, P. and Siminos, E. and Takeuchi, K. A.}, Journal = {Phys. Rev. Lett.}, Year = {2016}, Pages = {024101}, Volume = {117}, DOI = {10.1103/PhysRevLett.117.024101} } @Article{DDeSItz83, author = {B. Derrida and L. De Seze and C. Itzykson}, journal = {J. Stat Phys}, title = {Fractal structure of zeros in hierarchical models}, year = {1983}, pages = {559--569}, volume = {33}, doi = {10.1007/BF01018834}, } @Article{DDF00, author = {J. W. Demmel and L. Dieci and M. J. Friedman}, title = {Computing connecting orbits via an improved algorithm for continuing invariant spaces}, journal = {SIAM J. Sci. Comput.}, year = {2000}, volume = {22}, pages = {81--94}, doi = {10.1137/s1064827598344868}, } @InProceedings{DDS90, Title = {Automated pattern eduction from turbulent flow diagnostics}, Author = {D. D. Stretch}, Booktitle = {Annual Research Briefs}, Year = {1990}, Pages = {145--157}, Publisher = {Center for Turbulence Research, Stanford Univ.} } @Article{DeaMar06, author = {J. H. B. Deane and L. Marsh}, journal = {Phys. Lett. A}, title = {Unstable periodic orbit detection for {ODEs} with periodic forcing}, year = {2006}, pages = {555--558}, volume = {359}, doi = {10.1016/j.physleta.2006.06.088}, } @Article{DeGregorio85, Title = {The study of periodic orbits of dynamical systems. {The} use of a computer}, Author = {De Gregorio, S.}, Journal = {J. Stat. Phys.}, Year = {1985}, Pages = {947--972}, Volume = {38}, DOI = {10.1007/BF01010424} } @Article{DeLeo96, author = {De Leo, S.}, title = {Quaternionic electroweak theory}, journal = {J. Phys. G}, year = {1996}, volume = {22}, pages = {1137}, doi = {10.1088/0954-3899/22/8/004}, } @Article{DellFroSer00, Title = {On the isolated spectrum of the {Perron-Frobenius} operator}, Author = {M. Dellnitz and G. Froyland and S. Sertl}, Journal = {Nonlinearity}, Year = {2000}, Pages = {1171}, Volume = {13}, DOI = {10.1088/0951-7715/13/4/310} } @Article{DemaGasp09, Title = {Noise-induced escape from bifurcating attractors: {Symplectic} approach in the weak-noise limit}, Author = {Demaeyer, J. and Gaspard, P.}, Journal = {Phys. Rev. E}, Year = {2009}, Pages = {031147}, Volume = {80}, DOI = {10.1103/PhysRevE.80.031147} } @Article{DemaGasp13, Title = {A trace formula for activated escape in noisy maps}, Author = {J. Demaeyer and P. Gaspard}, Journal = {J. Stat. Mech.}, Year = {2013}, Pages = {P10026}, Volume = {2013}, DOI = {10.1088/1742-5468/2013/10/P10026} } @Misc{DemChaos, author = {E. Demidov}, title = {Chaotic maps}, year = {2009}, url = {http://www.ibiblio.org/e-notes/Chaos/contents.htm}, } @Article{DemMat01, author = {Demidenko, G. V. and Matveeva, I. I.}, journal = {Siberian Math. J.}, title = {On stability of solutions to linear systems with periodic coefficients}, year = {2001}, pages = {282--296}, volume = {42}, doi = {10.1023/A:1004837029765}, } @Misc{DemMset, author = {Demidov, E.}, title = {Anatomy of {Mandelbrot} and {Julia} sets}, year = {2015}, url = {http://www.ibiblio.org/e-notes/MSet/Contents.htm}, } @Book{Dennis96, title = {{Numerical Methods for Unconstrained Optimization and Nonlinear Equations}}, publisher = {SIAM}, year = {1996}, author = {Dennis, J. E. and Schnabel, R. B.}, addr = {Philadelphia}, doi = {10.1137/1.9781611971200}, } @Article{DePo11, author = {S. Denisov and A. V. Ponomarev}, title = {Oscillons: {An} encounter with dynamical chaos in 1953?}, journal = {Chaos}, year = {2011}, volume = {21}, pages = {023123}, doi = {10.1063/1.3562545}, } @Article{DeRonc95, Title = {Semiclassical approximation as a small-noise expansion}, Author = {A. Defendi and M. Roncadelli}, Journal = {J. Phys. A}, Year = {1995}, Pages = {515--520}, Volume = {28}, DOI = {10.1088/0305-4470/28/21/001} } @Article{DeScTi83, Title = {A rigorous study of periodic orbits by means of a computer}, Author = {De Gregorio, S. and Scoppola, E. and Tirozzi, B.}, Journal = {J. Stat. Phys.}, Year = {1983}, Pages = {25--33}, Volume = {32}, DOI = {10.1007/BF01009417} } @Article{detdiff1, Title = {Onset of diffusion and universal scaling in chaotic systems}, Author = {T. Geisel and J. Nierwetberg}, Journal = {Phys. Rev. Lett.}, Year = {1982}, Pages = {7}, Volume = {48}, DOI = {10.1103/PhysRevLett.48.7} } @Article{detect, author = {Champneys, A. R. and Kuznetsov, Y. A.}, title = {Numerical detection and continuation of codimension-two homoclinic bifurcations}, journal = {Int. J. Bifur. Chaos}, year = {1994}, volume = {4}, pages = {785--822}, doi = {10.1142/s0218127494000587}, } @Article{Dettm14, author = {Dettmann, C. P.}, title = {Diffusion in the {Lorentz} gas}, journal = {Commun. Theor. Phys}, year = {2014}, volume = {62}, pages = {521--540}, doi = {10.1088/0253-6102/62/4/10}, } @Book{deva87, author = {R. L. Devaney}, publisher = {Westview Press}, title = {{An Introduction to Chaotic Dynamical systems}}, year = {2008}, edition = {2}, doi = {10.2307/3619398}, } @Book{deva92, title = {{A First Course in Chaotic Dynamical Systems: Theory and Experiment}}, publisher = {Westview Press}, year = {1992}, author = {Devaney, R. L.}, isbn = {9780813345475}, doi = {10.2307/2324232}, } @Book{deva22, author = {R. L. Devaney}, publisher = {CRC Press}, title = {{An Introduction to Chaotic Dynamical systems}}, year = {2022}, edition = {3}, doi = {10.1201/9780429280801}, } @Article{Devaney79, author = {Devaney, R. L. and Nitecki, Z.}, journal = {Commun. Math. Phys.}, title = {Shift automorphisms in the {H{\'e}non} mapping}, year = {1979}, pages = {137--146}, volume = {67}, doi = {10.1007/BF01221362}, } @Incollection{devog58, author = {De Vog{\'e}laere, R. J.}, title = {On the structure of symmetric periodic solutions of conservative systems, with applications}, booktitle = {{Contribution to the Theory of Nonlinear Oscillations}}, publisher = {Princeton Univ. Press}, year = {1958}, editor = {S. Lefschetz}, isbn = {9781400881758}, pages = {53--84}, address = {Princeton NJ}, url = {http://www.jstor.org/stable/j.ctt1b9x0t9} } @Article{DFGHMS86, Title = {Chaotic streamlines in the {ABC} flows}, Author = {Dombre, T. and Frisch, U. and Greene, J. M. and H{\'e}non, M. and Mehr, A. and Soward, A. M.}, Journal = {J. Fluid Mech.}, Year = {1986}, Pages = {353--391}, Volume = {167}, DOI = {10.1017/S0022112086002859} } @Article{DGOY90, Title = {Transition to chaotic scattering}, Author = {Ding, M. and C. Grebogi and E. Ott and J. A. Yorke}, Journal = {Phys. Rev. A}, Year = {1990}, Pages = {7025--7040}, Volume = {42}, DOI = {10.1103/PhysRevA.42.7025} } @Book{DGS76, title = {{Ergodic Theory on Compact Spaces}}, publisher = {Springer}, year = {1976}, author = {M. Denker and C. Grillenberger and K. Sigmund}, doi = {10.1007/bfb0082364}, } @Article{DHBEks96, author = {H. Dankowicz and P. Holmes and G. Berkooz and J. Elezgaray}, title = {Local models of spatio-temporally complex fields}, journal = {Physica D}, year = {1996}, volume = {90}, pages = {387--407}, doi = {10.1016/0167-2789(95)00245-6}, } @Article{DhGoKu03, Title = {{MATCONT: A MATLAB} package for numerical bifurcation analysis of {ODEs}}, Author = {Dhooge, A. and Govaerts, W. and Kuznetsov, Yu. A.}, Journal = {ACM Trans. Math. Softw.}, Year = {2003}, Pages = {141--164}, Volume = {29}, DOI = {10.1145/779359.779362} } @Article{DhoPatZhi15, author = {G. Dhont and F. Patra and B. I. Zhilinski{\'i}}, journal = {J. Phys. A}, title = {The action of the special orthogonal group on planar vectors: integrity bases via a generalization of the symbolic interpretation of {Molien} functions}, year = {2015}, pages = {035201}, volume = {48}, doi = {10.1088/1751-8113/48/3/035201}, } @Article{DhoZhi13, Title = {The action of the orthogonal group on planar vectors: invariants, covariants and syzygies}, Author = {G. Dhont and B. I. Zhilinski{\'i}}, Journal = {J. Phys. A}, Year = {2013}, Pages = {455202}, Volume = {46}, DOI = {10.1088/1751-8113/46/45/455202} } @Book{Diacu96, title = {{Celestial Encounters: The Origins of Chaos and Stability}}, publisher = {Princeton Univ. Press}, year = {1996}, author = {Diacu, F. and Holmes, P.}, address = {Princeton, NJ}, isbn = {9780691005454}, } @Article{diag_Fred, Title = {Spectrum of stochastic evolution operators: {Local} matrix representation approach}, Author = {Cvitanovi{\'c}, P. and S{\o}ndergaard, N. and Palla, G. and Vattay, G. and Dettmann, C. P.}, Journal = {Phys. Rev. E}, Year = {1999}, Pages = {3936--3941}, Volume = {60}, DOI = {10.1103/PhysRevE.60.3936} } @Article{DiEl08, author = {Dieci, L. and Elia, C.}, title = {{SVD} algorithms to approximate spectra of dynamical systems}, journal = {Math. Comput. Simul.}, year = {2008}, volume = {79}, pages = {1235--1254}, doi = {10.1016/j.matcom.2008.03.005}, } @InProceedings{diepenbeek_continuation_????, author = {Vanderbauwhede, A.}, booktitle = {{Proc. {Equadiff 2003}}}, title = {Continuation and bifurcation of periodic orbits in symmetric {Hamiltonian} systems}, year = {2004}, editor = {F. Dumortier and et.al.}, url = {http://at.yorku.ca/c/a/l/o/73.htm}, } @Article{DingCvit14, Title = {Periodic eigendecomposition and its application in {Kuramoto-Sivashinsky} system}, Author = {Ding, X. and Cvitanovi{\'c}, P.}, Journal = {{SIAM} J. Appl. Dyn. Syst.}, Year = {2016}, Pages = {1434--1454}, Volume = {15}, DOI = {10.1137/15M1037299} } @Misc{DingKang16, author = {X. Ding and S. H. Kang}, title = {Adaptive time-stepping exponential integrators for cubic-quintic complex {Ginzburg--Landau} equations}, year = {2017}, eprint = {1703.09622}, eprinttype = {arxiv}, } @Article{DiRuVl97, author = {Dieci, L. and Russell, R. D. and Van Vleck, E. S.}, title = {On the compuation of {Lyapunov} exponents for continuous dynamical systems}, journal = {SIAM J. Numer. Anal.}, year = {1997}, volume = {34}, pages = {402--423}, doi = {10.1137/s0036142993247311}, } @Book{ditt01cq, title = {{Classical and Quantum Dynamics: From Classical Paths to Path Integrals}}, publisher = {Springer}, year = {1994}, author = {W. Dittrich and M. Reuter}, address = {New York}, } @Article{DJKLMPPRT05, author = {M. Dellnitz and O. Junge and W. S. Koon and F. Lekien and M. W. Lo and J. E. Marsden and K. Padberg and R. Preis and S. D. Ross and B. Thiere}, title = {Transport in dynamical astronomy and multibody problems}, journal = {Int. J. Bifur. Chaos}, year = {2005}, volume = {15}, pages = {699--727}, doi = {10.1142/S0218127405012545} } @Article{DJRV07, author = {Dieci, L. and Jolly, M. S. and Rosa, R. and Van Vleck, E. S.}, title = {Error in approximation of {Lyapunov} exponents on inertial manifolds: {The Kuramoto-Sivashinsky} equation}, journal = {Discrete Contin. Dynam. Systems}, year = {2008}, volume = {9}, pages = {555--580}, doi = {10.3934/dcdsb.2008.9.555}, } @Article{DLBconv92, author = {F. Daviaud and J. Lega and P. Berg{\'e} and P. Coullet and M. Dubois}, title = {Spatio-temporal intermittency in a 1{D} convective pattern: theoretical model and experiments}, journal = {Physica D}, year = {1992}, volume = {55}, pages = {287--308}, doi = {10.1016/0167-2789(92)90061-q}, } @Article{dlbd00, author = {R. L. Davidchack and Y-C Lai and E. M. Bollt and M. Dhamala}, title = {Estimating generating partitions of chaotic systems by unstable periodic orbits}, journal = {Phys. Rev. E}, year = {2000}, volume = {61}, pages = {1353}, doi = {10.1103/physreve.61.1353}, } @Article{DM97, Title = {Stability ordering; Strong field {Lorentz} gas}, Author = {C. P. Dettmann and G. P. Morriss}, Journal = {Phys. Rev. Lett.}, Year = {1997}, Pages = {4201--4204}, Volume = {78}, DOI = {10.1103/PhysRevLett.78.4201} } @Article{doeb94nls, author = {H.-D. Doebner and G. A. Goldin}, title = {Properties of nonlinear {Schr{\"{o}}dinger} equations associated with diffeomorphism group representations}, journal = {J. Phys. A}, year = {1994}, volume = {27}, pages = {1771--1780}, doi = {10.1088/0305-4470/27/5/036}, } @Article{doedel_computation_2003, author = {Doedel, E. J. and Paffenroth, R. C. and Keller, H. B. and Dichmann, D. J. and Galan, J. and Vanderbauwhede, A.}, title = {Computation of periodic solutions of conservative systems with application to the 3-body problem}, journal = {Int. J. Bifur. Chaos}, year = {2003}, volume = {13}, pages = {1353--1381}, doi = {10.1142/s0218127403007291}, } @Article{doedel_elemental_2007, author = {Doedel, E. J. and V. A. Romanov and R. C. Paffenroth and H. B. Keller and D. J. Dichmann and Galan, J. and Vanderbauwhede, A.}, title = {Elemental periodic orbits associated with the libration points in the circular restricted 3-{Body Problem}}, journal = {Int. J. Bifur. Chaos}, year = {2007}, volume = {17}, pages = {2625--2677}, doi = {10.1142/s0218127407018671}, } @Article{doelman91n, author = {A. Doelman}, title = {Finite-dimensional models of the {Ginzburg-Landau} equation}, journal = {Nonlinearity}, year = {1991}, volume = {4}, pages = {231--250}, doi = {10.1088/0951-7715/4/2/003}, } @Article{doercgl87, author = {C. R. Doering and J. D. Gibbon and D. D. Holm and B. Nikolaenko}, title = {Exact {Lyapunov} dimension of the universal attractor for the complex {Ginzburg-Landau} equation}, journal = {Phys. Rev. Lett.}, year = {1987}, volume = {59}, pages = {2911--2914}, doi = {10.1103/physrevlett.59.2911}, } @Article{doercgl88, author = {C. R. Doering and J. D. Gibbon and D. D. Holm and B. Nikolaenko}, title = {Low-dimensional behaviour in the complex {Ginzburg-Landau} equation}, journal = {Nonlinearity}, year = {1988}, volume = {1}, pages = {279--309}, doi = {10.1088/0951-7715/1/2/001}, } @Article{DoLa14, Title = {Organization of spatially periodic solutions of the steady {Kuramoto--Sivashinsky} equation}, Author = {C. Dong and Y. Lan}, Journal = {Commun. Nonlinear Sci. Numer. Simul.}, Year = {2014}, Pages = {2140--2153}, Volume = {19}, DOI = {10.1016/j.cnsns.2013.09.040} } @Article{DoLa14a, Title = {A variational approach to connecting orbits in nonlinear dynamical systems}, Author = {C. Dong and Y. Lan}, Journal = {Phys. Lett. A}, Year = {2014}, Pages = {705--712}, Volume = {378}, DOI = {10.1016/j.physleta.2014.01.001} } @Article{DolPol98, author = {Dolgopyat, D. and Pollicott, M.}, journal = {Ergod. Theor. Dynam. Syst.}, title = {Addendum to ``{Periodic} orbits and dynamical spectra''}, year = {1998}, pages = {293--301}, volume = {18}, doi = {10.1017/s0143385798113913}, } @Article{Donaldson09c, author = {Donaldson, A. F.}, title = {Vector symmetry reduction}, journal = {Electronic Notes in Theoretical Computer Science}, year = {2009}, volume = {250}, pages = {3--18}, note = {Proceedings of the Eighth International Workshop on Automated Verification of Critical Systems (AVoCS 2008)}, doi = {10.1016/j.entcs.2009.08.014}, } @InCollection{Donnay88, author = {Donnay, V. J.}, booktitle = {Dynamical Systems}, publisher = {Springer}, title = {Geodesic flow on the two-sphere, {Part {II}: Ergodicity}}, year = {1988}, address = {New York}, editor = {Alexander, J. C.}, pages = {112--153}, series = {Lect. Notes Math.}, volume = {1342}, doi = {10.1007/BFb0082827}, } @Article{Doob42, Title = {The {Brownian} movement and stochastic equations}, Author = {J. L. Doob}, Journal = {Ann. Math.}, Year = {1942}, Pages = {351--369}, Volume = {43}, DOI = {10.2307/1968873} } @Book{Dorf98, author = {J. R. Dorfman}, publisher = {Cambridge Univ. Press}, title = {{An Introduction to Chaos in Nonequilibrium Statistical Mechanics}}, year = {1999}, address = {Cambridge UK}, doi = {10.1017/cbo9780511628870}, } @Book{Doug, title = {{Banach Algebra Techniques in Operator Theory}}, publisher = {Springer}, year = {1998}, author = {G. Douglas}, address = {New York}, doi = {10.1007/978-1-4612-1656-8}, } @Article{Doyon05, author = {Doyon, B. and Dub{\'e}, L. J.}, title = {On {J}acobian matrices for flows}, journal = {Chaos}, year = {2005}, volume = {15}, pages = {013108}, doi = {10.1063/1.1854031} } @Article{DR_prl, Title = {Existence of stable orbits in the {$x^{2}y^{2}$} potential}, Author = {P. Dahlqvist and G. Russberg}, Journal = {Phys. Rev. Lett.}, Year = {1990}, Pages = {2837--2838}, Volume = {65}, DOI = {10.1103/PhysRevLett.65.2837} } @Book{DR81, author = {P. Drazin and W. H. Reid}, publisher = {Cambridge Univ. Press}, title = {{Hydrodynamic Stability}}, year = {1981}, address = {Cambridge UK}, isbn = {9780521009652}, doi = {10.1017/cbo9780511616938}, } @Article{DR91a, author = {P. Dahlqvist and G. Russberg}, journal = {J. Phys. A}, title = {Periodic orbit quantization of bound chaotic systems}, year = {1991}, pages = {4763--4778}, volume = {24}, doi = {10.1088/0305-4470/24/20/012}, } @Article{Dragt05, Title = {The symplectic group and classical mechanics}, Author = {Dragt, A. J.}, Journal = {Ann. New York Acad. Sci.}, Year = {2005}, Pages = {291--307}, Volume = {1045}, DOI = {10.1196/annals.1350.025} } @Unpublished{Dragt11, author = {A. J. Dragt}, title = {{Lie Methods for Nonlinear Dynamics with Applications to Accelerator Physics}}, year = {2011}, institution = {Physics Department, U. of Maryland}, url = {http://www.physics.umd.edu/dsat/dsatliemethods.html}, } @TechReport{Dragt11bad, author = {Dragt, A. J.}, institution = {{Physics Department, U. of Maryland}}, title = {Lie methods for nonlinear dynamics with applications to accelerator physics}, year = {2011}, url = {http://www.physics.umd.edu/dsat/dsatliemethods.html}, } @Misc{DraHab08, author = {Dragt, A. J. and Habib, S.}, title = {How {Wigner} functions transform under symplectic maps}, year = {1998}, eprint = {quant-ph/9806056}, eprintclass = {quant-ph}, eprinttype = {arxiv}, } @Book{Dresner98, title = {{Applications of Lie's Theory of Ordinary and Partial Differential Equations}}, publisher = {CRC Press}, year = {1998}, author = {Dresner, L.}, isbn = {9781420050783}, address = {Boca Raton FL}, doi = {10.1201/9781420050783}, } @Book{Dresselhaus07, Title = {{Group Theory: Application to the Physics of Condensed Matter}}, Author = {Dresselhaus, M. S. and Dresselhaus, G. and Jorio, A.}, Publisher = {Springer}, Year = {2007}, Address = {New York}, DOI = {10.1007/978-3-540-32899-5} } @Article{Driebe96, author = {D. J. Driebe and G. E. Ordnez}, title = {Using symmetries of the {Frobenius-Perron} operator to determine spectral decompositions}, journal = {Phys. Lett. A}, year = {1996}, volume = {211}, pages = {204--210}, doi = {10.1016/0375-9601(96)00006-0}, } @Book{Driebe99, author = {Driebe, D. J.}, publisher = {Springer}, title = {{Fully Chaotic Maps and Broken Time Symmetry}}, year = {1999}, address = {New York}, isbn = {0792355644}, doi = {10.1007/978-94-017-1628-4}, } @Misc{DSWeb, author = {{SIAG Dynamical Systems}}, title = {{DSWeb Dynamical Systems Software}}, year = {2015}, institution = {SIAM}, url = {http://www.dynamicalsystems.org/sw/sw/}, } @Article{du87, author = {M. L. Du and J. B. Delos}, title = {Effect of closed classical orbits on quantum spectra: {Ionization} of atoms in a magnetic field}, journal = {Phys. Rev. Lett.}, year = {1987}, volume = {58}, pages = {1731}, doi = {10.1103/physrevlett.58.1731}, } @Book{Duffing, title = {{Erzwungene Schwingungen bei ver{\"a}nderlicher Eigenfrequenz und ihre technische Bedeutung}}, publisher = {Vieweg und Sohn}, year = {1918}, author = {Duffing, G.}, number = {41-42}, address = {Braunschweig}, } @Article{DuIbKo06, Title = {Cocoon bifurcation in three-dimensional reversible vector fields}, Author = {Dumortier, F. and Ibanez, S. and Kokubu, H.}, Journal = {Nonlinearity}, Year = {2006}, Pages = {305--328}, Volume = {19}, DOI = {10.1088/0951-7715/19/2/004} } @Article{DuiGui75, author = {Duistermaat, J. J. and Guillemin, V. W.}, title = {The spectrum of positive elliptic operators and periodic bicharacteristics}, journal = {Inv. Math.}, year = {1975}, volume = {29}, pages = {39--79}, doi = {10.1007/BF01405172}, } @Book{DuiKol00, title = {{Lie Groups}}, publisher = {Springer}, year = {2000}, author = {Duistermaat, J. J. and Kolk, J. A. C.}, isbn = {9783642569364}, address = {New York}, doi = {10.1007/978-3-642-56936-4}, } @Article{Dul96a, Title = {A two-parameter study of the extent of chaos in a billiard system}, Author = {H. R. Dullin and P. H. Richter and A. Wittek}, Journal = {Chaos}, Year = {1996}, Pages = {43--58}, Volume = {6}, DOI = {10.1063/1.166156} } @Article{Dul96b, author = {H. R. Dullin}, title = {Linear stability in billiards with potential}, journal = {Nonlinearity}, year = {1998}, volume = {11}, pages = {151--173}, doi = {10.1088/0951-7715/11/1/010}, } @Article{dullin-2008, Title = {Quadratic volume-preserving maps: {Invariant} circles and bifurcations}, Author = {H. R. Dullin and J. D. Meiss}, Journal = {SIAM J. Appl. Dyn. Syst.}, Year = {2008}, Pages = {76--128}, Volume = {8}, DOI = {10.1137/080728160} } @Article{DuOtt1993, author = {Du, Y. and Ott, E.}, title = {Growth rates for fast kinematic dynamo instabilities of chaotic fluid flows}, journal = {J. Fluid Mech.}, year = {1993}, volume = {257}, pages = {265--288}, doi = {10.1017/s0022112093003076}, } @Article{DurBeh97, author = {A. D{\"u}ring and U. Behn}, journal = {Phys. Lett. A}, title = {Selective stabilisation of very long unstable periodic orbits in chaotic systems}, year = {1997}, pages = {177--182}, volume = {230}, doi = {10.1016/S0375-9601(97)00237-5}, } @Article{Duval88, author = {J.-P. Duval}, journal = {Theor. Comput. Sci.}, title = {Generation d'une section des classes de conjugaison et arbre des mots de {Lyndon} de longueur born{\'e}}, year = {1988}, pages = {255--283}, volume = {60}, doi = {10.1016/0304-3975(88)90113-2}, } @Article{DV02, author = {D. Viswanath}, title = {The {Lindstedt-Poincar{\'e}} technique as an algorithm for finding periodic orbits}, journal = {SIAM Rev.}, year = {2001}, volume = {43}, pages = {478--495}, doi = {10.1137/S0036144500375292}, } @Article{DV03, Title = {Symbolic dynamics and periodic orbits of the {Lorenz} attractor}, Author = {D. Viswanath}, Journal = {Nonlinearity}, Year = {2003}, Pages = {1035--1056}, Volume = {16}, DOI = {10.1088/0951-7715/16/3/314} } @Article{DV04, author = {D. Viswanath}, title = {The fractal property of the {Lorenz} attractor}, journal = {Physica D}, year = {2004}, volume = {190}, pages = {115--128}, doi = {10.1016/j.physd.2003.10.006}, } @Article{DV2000, author = {O. Dauchot and N. Vioujard}, title = {Phase space analysis of a dynamical model for the subcritical transition to turbulence in plane {Couette} flow}, journal = {Eur. Phys. J. B}, year = {2000}, volume = {14}, pages = {377--381}, doi = {10.1007/s100510050142}, } @Article{DVY93, Title = {Chaotic scattering on a double well: {Periodic} orbits, symbolic dynamics, and scaling}, Author = {V. Daniels and M. Valli{\`e}res and J.-M. Yuan}, Journal = {Chaos}, Year = {1993}, Pages = {475--485}, Volume = {3}, DOI = {10.1063/1.165953} } @Article{EaPoSa10, author = {J. Early and J. Pohjanpelto and R. Samelson}, title = {Group foliation of equations in geophysical fluid dynamics}, journal = {Discrete Contin. Dyn. Syst.}, year = {2010}, volume = {27}, pages = {1571--1586}, doi = {10.3934/dcds.2010.27.1571}, } @Incollection{Earn, author = {J. D. Earn}, title = {Symplectic integration without roundoff error}, booktitle = {{Ergodic Concepts in Stellar Dynamics}}, publisher = {Springer Nature}, year = {2006}, pages = {122--130}, doi = {10.1007/bfb0058098}, } @Article{EAS87, author = {E. A. Spiegel}, title = {Chaos: {A} mixed metaphor for turbulence}, journal = {Proc. R. Soc. Lond. A}, year = {1987}, volume = {A413}, pages = {87}, doi = {10.1515/9781400860197.87}, } @Article{Easton86, author = {R. W. Easton}, title = {Trellises formed by stable and unstable manifolds in the plane}, journal = {Trans. Amer. Math. Soc.}, year = {1986}, volume = {294}, pages = {719--732}, doi = {10.1090/S0002-9947-1986-0825732-X}, } @Article{Eben02, author = {E. Ben-Naim and P. L. Krapivsky}, title = {Growth and structure of stochastic sequences}, journal = {J. Phys. A}, year = {2002}, volume = {35}, pages = {L557--L563}, doi = {10.1088/0305-4470/35/41/101}, } @Article{ech, author = {D. J. Evans and E. G. D. Cohen and G. P. Morris}, journal = {Phys. Rev. A}, title = {Viscosity of a simple fluid from its maximal {Lyapunov} exponents}, year = {1990}, pages = {5990--5997}, volume = {42}, doi = {10.1103/PhysRevA.42.5990}, } @Article{eck81, author = {J.-P. Eckmann}, title = {Roads to turbulence in dissipative dynamical systems}, journal = {Rev. Mod. Phys.}, year = {1981}, volume = {53}, pages = {643}, doi = {10.1103/revmodphys.53.643}, } @Article{eckcgl, author = {B. Janiaud and A. Pumir and D. Bensimon and V. Croquette and H. Richter and L. Kramer}, title = {The {Eckhaus} instability for traveling waves}, journal = {Physica D}, year = {1992}, volume = {55}, pages = {269--286}, doi = {10.1016/0167-2789(92)90060-z}, } @Article{EckHoPo89, author = {B. Eckhardt and G. Hose and E. Pollak}, title = {Quantum mechanics of a classically chaotic system: {Observations} on scars, periodic orbits, and vibrational adiabaticity}, journal = {Phys. Rev. A}, year = {1989}, volume = {39}, pages = {3776--3793}, doi = {10.1103/PhysRevA.39.3776}, } @Article{EckKamp86, Title = {Liapunov exponents from time series}, Author = {J.-P. Eckmann and S. O. Kamphorst and D. Ruelle and S. Ciliberto}, Journal = {Phys. Rev. A}, Year = {1986}, Pages = {4971--4979}, Volume = {34}, DOI = {10.1103/PhysRevA.34.4971} } @Article{ecklp88, author = {J. -P. Eckmann and C. E. Wayne}, title = {Liapunov spectra for infinite chains of nonlinear oscillators}, journal = {J. Stat. Phys.}, year = {1988}, volume = {50}, pages = {853--878}, doi = {10.1007/bf01019144}, } @Book{eckman80map, title = {{Iterated Maps on the Interval as Dynamical Systems}}, publisher = {Birkh{\"{a}}user}, year = {2009}, author = {P. Collet and J.-P. Eckman}, address = {Boston}, doi = {10.1007/978-0-8176-4927-2}, } @Article{EckmannRuelle1985, Title = {Ergodic theory of chaos and strange attractors}, Author = {J.-P. Eckmann and D. Ruelle}, Journal = {Rev. Mod. Phys.}, Year = {1985}, Pages = {617--656}, Volume = {57}, DOI = {10.1103/RevModPhys.57.617} } @Article{EckmannRuelle1992, Title = {Fundamental limitations for estimating dimensions and {Lyapunov} exponents in dynamical systems}, Author = {J.-P. Eckmann and D. Ruelle}, Journal = {Physica D}, Year = {1992}, Pages = {185--187}, Volume = {56}, DOI = {10.1016/0167-2789(92)90023-G}, URL = {http://www.ihes.fr/~ruelle/PUBLICATIONS/[106].pdf} } @Article{EckOtt94, Title = {Periodic orbit analysis of the {Lorenz} flow}, Author = {B. Eckhardt and G. Ott}, Journal = {Z. Phys. B}, Year = {1994}, Pages = {259--266}, Volume = {93}, DOI = {10.1007/BF01316970} } @Article{EckWi90, author = {B. Eckhardt and D. Wintgen}, journal = {J. Phys. B}, title = {Symbolic description of periodic orbits for the quadratic {Zeeman} effect}, year = {1990}, pages = {355--363}, volume = {23}, doi = {10.1088/0953-4075/23/3/007}, } @Book{Efst05, title = {{Metamorphoses of {Hamiltonian} systems with {Symmetries}}}, publisher = {Springer}, year = {2005}, author = {K. Efstathiou}, address = {New York}, doi = {10.1007/b105138}, } @Article{EG, author = {B. Eckhardt and S. Grossmann}, title = {Correlation functions in chaotic systems from periodic orbits}, journal = {Phys. Rev. E}, year = {1994}, doi = {10.1103/physreve.50.4571}, } @Article{EG05, author = {Endler, A. and Gallas, J. A. C.}, journal = {Phys. Lett. A}, title = {Reductions and simplifications of orbital sums in a {Hamiltonian} repeller}, year = {2006}, pages = {124--128}, volume = {352}, doi = {10.1016/j.physleta.2006.01.031}, } @Article{EG05a, author = {Endler, A. and Gallas, J. A. C.}, journal = {Phys. Lett. A}, title = {Conjugacy classes and chiral doublets in the {H{\'e}non Hamiltonian} repeller}, year = {2006}, pages = {1--7}, volume = {356}, doi = {10.1016/j.physleta.2006.04.042}, } @Article{eg2006c, author = {A. Endler and J. A. C. Gallas}, title = {Mandelbrot-like sets in dynamical systems with no critical points}, journal = {Compt. Rend. Acad. Sci., Math. (Paris)}, year = {2006}, volume = {342}, pages = {681--684}, doi = {10.1016/j.crma.2006.02.027} } @Article{egolf00, author = {D. A. Egolf and I. V. Melnikov and W. Pesch and R. E. Ecke}, journal = {Nature}, title = {Mechanisms of extensive spatiotemporal chaos in {Rayleigh-Benard} convection}, year = {2000}, pages = {733--736}, volume = {404}, doi = {10.1038/35008013}, } @Article{egolf94, Title = {Relation between fractal dimension and spatial correlation length for extensive chaos}, Author = {D. A. Egolf and H. S. Greenside}, Journal = {Nature}, Year = {1994}, Pages = {129--131}, Volume = {369}, DOI = {10.1038/369129a0} } @Article{egolf98, author = {D. A. Egolf and I. V. Melnikov and E. Bodenschatz}, title = {Importance of local pattern properties in spiral defect chaos}, journal = {Phys. Rev. Lett.}, year = {1998}, volume = {80}, pages = {3228}, doi = {10.1103/physrevlett.80.3228}, } @Article{EGtran95, author = {D. A. Egolf and H. S. Greenside}, journal = {Phys. Rev. Lett.}, title = {Characterization of the transition from defect to phase turbulence}, year = {1995}, pages = {1751}, volume = {74}, abtract = {For the CGLe on a large periodic interval, the transition from defect to phase turbulence is continuous. The conclusion is based on the calculation of the defect density, {Lyapunov} dimension density and correlation lengths.}, doi = {10.1103/physrevlett.74.1751}, } @InCollection{eigendensity, author = {R. Artuso and H. H. Rugh and P. Cvitanovi{\'c}}, title = {Why does it work?}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2020}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/paper.shtml#converg}, } @InCollection{Einst1917, author = {A. Einstein}, title = {On the quantum theorem of {Sommerfeld} and {Epstein}}, booktitle = {{The Collected Papers of {Albert Einstein: The Berlin} Years: Writings (1914-1917)}}, publisher = {Princeton Univ. Press}, year = {1917}, volume = {6}, pages = {443}, address = {Princeton NJ}, note = {E. Schucking, English translation of {``Zum Quantensatz von Sommerfeld und Epstein,''} {Verh. Deutsch. Phys. Ges.} {19}, 82}, isbn = {9780691017341}, } @Article{Einstein05, author = {A. Einstein}, title = {{{\"U}}ber die von der molekularkinetischen {Theorie der W\"arme geforderte Bewegung von in ruhenden Fl\"ussigkeiten suspendierten Teilchen}}, journal = {Ann. Phys.}, year = {1905}, volume = {17}, pages = {549--560}, doi = {10.1002/andp.19053220806}, } @Article{EKO04, author = {J. P. England and B. Krauskopf and H. M. Osinga}, title = {Computing one-dimensional stable and unstable sets of planar maps without the inverse}, journal = {SIAM J. Appl. Dyn. Syst.}, year = {2004}, volume = {3}, pages = {161--190}, doi = {10.1137/030600131}, } @Article{EKR87, author = {Eckmann, J.-P. and Kamphorst, S. O. and Ruelle, D.}, title = {Recurrence plots of dynamical systems}, journal = {Europhys. Lett.}, year = {1987}, volume = {4}, pages = {973--977}, doi = {10.1209/0295-5075/4/9/004}, } @Book{EllDaw79, author = {Elliott, J. P. and Dawber, P. G.}, publisher = {MacMillan}, title = {{Symmetry in Physics}}, year = {1979}, address = {Surrey}, volume = {2}, doi = {10.1007/978-1-349-07635-2}, } @Article{EllGaHoRa09, author = {Ellis, D. C. P. and Gay-Balmaz, F. and Holm, D. D. and Ratiu, T. S.}, title = {{Lagrange-Poincar{\'e}} field equations}, journal = {J. Geom. Phys.}, year = {2011}, volume = {61}, pages = {2120--2146}, doi = {10.1016/j.geomphys.2011.06.007}, } @Book{ellip, title = {{Elliptic Functions and Applications}}, publisher = {Springer}, year = {1989}, author = {D. F. Lawden}, address = {New York}, doi = {10.1007/978-1-4757-3980-0}, } @Article{Elyutin04, author = {Elyutin, P. V.}, title = {{Lyapunov} exponent for a gas of soft scatterers}, journal = {Phys. Lett. A}, year = {2004}, volume = {331}, pages = {153--156}, doi = {10.1016/j.physleta.2004.08.043} } @Article{EM99, author = {B. Eckhardt and A. Mersmann}, title = {Transition to turbulence in a shear flow}, journal = {Phys. Rev. E}, year = {1999}, volume = {60}, pages = {509--517}, doi = {10.1103/physreve.60.509}, } @Book{encDicMath, title = {{Encyclopedic Dictionary of Mathematics}}, publisher = {MIT press}, year = {1993}, author = {It{\^o}, K.}, isbn = {9780262590204}, } @Article{EndGal06, Title = {Reductions and simplifications of orbital sums in a {Hamiltonian} repeller}, Author = {A. Endler and J. A. C. Gallas}, Journal = {Phys. Lett. A}, Year = {2006}, Pages = {124--128}, Volume = {352}, DOI = {10.1016/j.physleta.2006.01.031} } @Article{entro, Title = {Computing the {Kolmogorov} entropy from time signals of dissipative and conservative dynamical systems}, Author = {Cohen, A. and Procaccia, I.}, Journal = {Phys. Rev. A}, Year = {1985}, Pages = {1872--1882}, Volume = {31}, DOI = {10.1103/PhysRevA.31.1872} } @Article{EpsLas81, author = {Epstein, H. and Lascoux, J.}, title = {Analyticity properties of the {Feigenbaum} function}, journal = {Commun. Math. Phys.}, year = {1981}, volume = {81}, doi = {10.1007/BF01209078}, } @Article{ER81, Title = {The {Lorenz} model and the method of {Carleman} embedding}, Author = {R. F. S. Andrade and A. Rauh}, Journal = {Phys. Lett. A}, Year = {1981}, Pages = {276--278}, Volume = {82}, DOI = {10.1016/0375-9601(81)90644-7} } @Article{ER92, Title = {Resummation of classical and semiclassical periodic-orbit formulas}, Author = {Eckhardt, B. and Russberg, G.}, Journal = {Phys. Rev. E}, Year = {1993}, Pages = {1578--1588}, Volume = {47}, DOI = {10.1103/PhysRevE.47.1578} } @Article{ErshPot98, Title = {On the concept of stationary {Lyapunov} basis}, Author = {S. V. Ershov and A. B. Potapov}, Journal = {Physica D}, Year = {1998}, Pages = {167--198}, Volume = {118}, DOI = {10.1016/S0167-2789(98)00013-X} } @Book{er-sinai, author = {Sinai, Ya. G.}, publisher = {Princeton Univ. Press}, title = {{Topics in Ergodic Theory}}, year = {1994}, address = {Princeton}, isbn = {9780691032771}, doi = {10.1063/1.2808677}, } @Article{ERTW91, Title = {Semiclassical cycle expansion for the helium atom}, Author = {G. S. Ezra and K. Richter and G. Tanner and D. Wintgen}, Journal = {J. Phys. B}, Year = {1991}, Pages = {L413--L420}, Volume = {24}, DOI = {10.1088/0953-4075/24/17/001} } @Inproceedings{etc12, author = {Cvitanovi{\'c}, P. and Gibson, J. F.}, title = {Geometry of state space in plane {Couette} flow}, booktitle = {{Advances in Turbulence XII}}, year = {2009}, editor = {B. Eckhardt}, series = {Proc. 12\textsuperscript{th} EUROMECH Eur. Turb. Conf., Marburg}, pages = {75--78}, address = {Berlin}, publisher = {Springer}, doi = {10.1007/978-3-642-03085-7-17}, } @Article{exac_diff, author = {H.-C. Tseng and H.-J. Chen and P.-C. Li and W.-Y. Lai and C.-H. Chou and H.-W. Che}, journal = {Phys. Lett. A}, title = {Some exact results for the diffusion coefficients of maps with pruning cycles}, year = {1994}, pages = {74--80}, volume = {195}, doi = {10.1016/0375-9601(94)90429-4}, } @Article{expholm88, author = {P. Holmes and J. Marsden and J. Scheurle}, title = {Exponentially small splittings of separatrices with applications to {KAM} theory and degenerate bifurcations}, journal = {Contemp. Math.}, year = {1988}, volume = {81}, pages = {213--244}, doi = {10.1090/conm/081/986267}, } @Article{FainSemi83, author = {V. Ya. Fainberg and A. M. Semikhatov}, journal = {Nucl. Phys. B}, title = {Instanton-centred expansions and elimination of zero modes}, year = {1983}, pages = {253--268}, volume = {226}, doi = {10.1016/0550-3213(83)90471-6}, } @Phdthesis{Familton15, Title = {{Quaternions: A History of Complex Noncommutative Rotation Groups in Theoretical Physics}}, Author = {Familton, J. C.}, School = {Dept. Mathematics Education, Columbia Univ.}, Year = {2015}, Address = {New York, NY}, DOI = {10.7916/D8FB521P} } @Article{Fang94, author = {H. P. Fang}, title = {Dynamics for a two-dimensional antisymmetric map}, journal = {J. Phys. A}, year = {1994}, volume = {27}, pages = {5187--5200}, doi = {10.1088/0305-4470/27/15/018} } @Article{Faraday1831, author = {Faraday, M.}, journal = {Phil. Trans. Roy. Soc.}, title = {On a peculiar class of acoustical figures; And on certain forms assumed by groups of particles upon vibrating elastic surfaces}, year = {1831}, pages = {299--340}, volume = {121}, doi = {10.1098/rstl.1831.0018}, } @Article{Farantos96, Title = {Exploring molecular vibrational motions with periodic orbits}, Author = {S. C. Farantos}, Journal = {Int. Rev. Phys. Chem.}, Year = {1996}, Pages = {345--374}, Volume = {15}, DOI = {10.1080/01442359609353188} } @Article{Farantos98, author = {S. C. Farantos}, journal = {Computer Phys. Comm.}, title = {{POMULT}: {A} program for computing periodic orbits in {Hamiltonian} systems based on multiple shooting algorithms}, year = {1998}, pages = {240}, volume = {108}, doi = {10.1016/S0010-4655(97)00131-8}, } @Article{farmer87, author = {J. D. Farmer and J. J. Sidorowich}, title = {Predicting chaotic time series}, journal = {Phys. Rev. Lett.}, year = {1987}, volume = {59}, pages = {845}, doi = {10.1103/physrevlett.59.845}, } @Article{fatou, Title = {Sur les {\'e}quations fonctionnelles}, Author = {P. Fatou}, Journal = {Bull. Soc. Math. France}, Year = {1919}, Pages = {161--271}, Volume = {47}, URL = {http://eudml.org/doc/86391} } @Article{fatou2, author = {P. Fatou}, title = {Sur les {\'e}quations fonctionnelles}, journal = {Bull. Soc. Math. France}, year = {1920}, volume = {48}, pages = {33--94}, url = {http://eudml.org/doc/86407}, } @Article{fatou3, author = {P. Fatou}, title = {Sur les {\'e}quations fonctionnelles}, journal = {Bull. Soc. Math. France}, year = {1920}, volume = {48}, pages = {208--314}, url = {http://eudml.org/doc/86405}, } @Article{FE03, Title = {Traveling waves in pipe flow}, Author = {H. Faisst and B. Eckhardt}, Journal = {Phys. Rev. Lett.}, Year = {2003}, Pages = {224502}, Volume = {91}, DOI = {10.1103/PhysRevLett.91.224502} } @Article{Fe86, author = {K. Feng}, title = {http://dl.acm.org/citation.cfm?id=8528.8538}, journal = {J. Comput. Math.}, year = {1986}, volume = {4}, pages = {279--289}, url = {http://dl.acm.org/citation.cfm?id=8528}, } @Article{Feffer83, Title = {The uncertainty principle}, Author = {C. L. Fefferman}, Journal = {Bull. Amer. Math. Soc.}, Year = {1983}, Pages = {129--206}, Volume = {9}, DOI = {10.1090/S0273-0979-1983-15154-6} } @Article{FeHa82, Title = {Irrational decimations and path-integrals for external noise}, Author = {M. J. Feigenbaum and B. Hasslacher}, Journal = {Phys. Rev. Lett.}, Year = {1982}, Pages = {605--609}, Volume = {49}, DOI = {10.1103/PhysRevLett.49.605} } @Article{feigen78, Title = {Quantitative universality for a class of nonlinear transformations}, Author = {M. J. Feigenbaum}, Journal = {J. Stat. Phys.}, Year = {1978}, Pages = {25--52}, Volume = {19}, DOI = {10.1007/BF01020332} } @Article{Feigenbaum87, Title = {Some characterizations of strange sets}, Author = {Feigenbaum, M. J.}, Journal = {J. Stat. Phys.}, Year = {1987}, Pages = {919--924}, Volume = {46}, DOI = {10.1007/BF01011148} } @Article{Feigenbaum88, Title = {Presentation functions, fixed points, and a theory of scaling function dynamics}, Author = {Feigenbaum, M. J.}, Journal = {J. Stat. Phys.}, Year = {1988}, Pages = {527--569}, Volume = {52}, DOI = {10.1007/BF01019716} } @Article{Feigenbaum88a, Title = {Presentation functions and scaling function theory for circle maps}, Author = {M. J. Feigenbaum}, Journal = {Nonlinearity}, Year = {1988}, Pages = {577--602}, Volume = {1}, DOI = {10.1088/0951-7715/1/4/005} } @InProceedings{FeigKen83, author = {M. J. Feigenbaum and R. D. Kenway}, title = {The onset of chaos}, booktitle = {{Statistical and Particle Physics: Common Problems and Techniques. Proc. 26th Scottish Universities Summer School in Physics}}, year = {1984}, editor = {Bowler, K. C. and McKane, A. J.}, pages = {1--100}, address = {Edinburgh}, publisher = {SUSSP} } @Article{FeigTsve82, Title = {Hidden supersymmetry in stochastic dissipative dynamics}, Author = {M. V. Feigel'man and A. M. Tsvelik}, Journal = {Sov. Phys. JETP}, Year = {1982}, Pages = {823}, Volume = {56}, URL = {http://www.jetp.ac.ru/cgi-bin/dn/e_056_04_0823.pdf} } @Article{feit, author = {S. D. Feit}, title = {Characteristic exponents and strange attractors}, journal = {Commun. Math. Phys.}, year = {1978}, volume = {61}, pages = {249--260}, doi = {10.1007/BF01940767}, } @Book{FellII, author = {Feller, W.}, publisher = {Wiley}, title = {{An Introduction to Probability Theory and Its Applications}}, year = {1971}, edition = {2}, isbn = {978-0-471-25709-7}, doi = {10.2307/1267002}, } @Article{FelsOlver98, Title = {Moving coframes: {I. A} practical algorithm}, Author = {M. Fels and P. J. Olver}, Journal = {Acta Appl. Math.}, Year = {1998}, Pages = {161--213}, Volume = {51}, DOI = {10.1023/A:1005878210297} } @Article{FelsOlver99, Title = {Moving coframes: {II. R}egularization and theoretical foundations}, Author = {M. Fels and P. J. Olver}, Journal = {Acta Appl. Math.}, Year = {1999}, Pages = {127--208}, Volume = {55}, DOI = {10.1023/A:1006195823000} } @Article{Fermi, Title = {On the origin of the cosmic radiation}, Author = {E. Fermi}, Journal = {Phys. Rev.}, Year = {1949}, Pages = {1169--1174}, Volume = {75}, DOI = {10.1103/PhysRev.75.1169} } @Book{Feynman65, author = {R. P. Feynman and A. R. Hibbs}, publisher = {Dover Publications Inc.}, title = {{Quantum Mechanics and Path Integrals}}, year = {1965}, address = {New York}, isbn = {9780486477220}, } @Article{FGZ93, Title = {Characterization of the {Lorenz} attractor by unstable periodic orbits}, Author = {V. Franceschini and C. Giberti and Z. M. Zheng}, Journal = {Nonlinearity}, Year = {1993}, Pages = {251--258}, Volume = {6}, DOI = {10.1088/0951-7715/6/2/006} } @Article{FI87, Title = {Theory of diffusion and intermittency in chaotic systems. {III: New} approach to temporal correlations}, Author = {H. Fujisaka and M. Inoue}, Journal = {Progr. Theor. Phys.}, Year = {1987}, Pages = {268--281}, Volume = {78}, DOI = {10.1143/PTP.78.268} } @Article{FI87b, Title = {Continued fraction expansion of fluctuation spectrum and generalized time correlation}, Author = {H. Fujisaka and M. Inoue}, Journal = {Progr. Theor. Phys}, Year = {1987}, Pages = {1203--1208}, Volume = {78}, DOI = {10.1143/PTP.78.1203} } @Article{Fici2006, author = {G. Fici and F. Mignosi and A. Restivo and M. Sciortino}, title = {Word assembly through minimal forbidden words}, journal = {Theor. Comput. Sci.}, year = {2006}, volume = {359}, pages = {214--230}, doi = {10.1016/j.tcs.2006.03.006} } @Article{Field70, Title = {Equivariant dynamical systems}, Author = {M. Field}, Journal = {Bull. Amer. Math. Soc.}, Year = {1970}, Pages = {1314--1318}, Volume = {76}, DOI = {10.1090/S0002-9947-1980-0561832-4} } @Incollection{Field88, author = {M. Field}, title = {Local structure of equivariant dynamics}, booktitle = {{Singularity Theory and its Applications: Warwick 1989, Part II: Singularities, Bifurcations and Dynamics}}, publisher = {Springer}, year = {1996}, editor = {M. Roberts and I. Stewart}, isbn = {9783540470472}, pages = {142--166}, address = {New York}, doi = {10.1007/BFb0085422}, } @Article{Field96, author = {M. Field}, title = {Symmetry breaking for compact {Lie} groups}, journal = {Memoirs Amer. Math. Soc.}, year = {1996}, volume = {120}, pages = {R8}, doi = {10.1090/memo/0574}, } @Article{FiGaLeLl16, author = {Figueras, J.-L. and Gameiro, M. and Lessard, J. P. and {de la Llave}, R.}, journal = {{SIAM} Journal on Applied Dynamical Systems}, title = {A framework for the numerical computation and a posteriori verification of invariant objects of evolution equations}, year = {2017}, pages = {1070--1088}, volume = {16}, doi = {10.1137/16m1073777}, } @Misc{FigLla16, author = {Figueras, J.-L. and {de la Llave}, R.}, title = {Numerical computations and computer assisted proofs of periodic orbits of the {Kuramoto-Sivashinsky} equation}, year = {2016}, eprint = {1605.01085}, eprinttype = {arxiv}, } @Article{Finkel96, author = {Finkelstein, D. R.}, title = {{Quaternionic Quantum Mechanics and Quantum Fields, by S. L. Adler}}, journal = {Phys. Today}, year = {1996}, volume = {49}, pages = {58}, doi = {10.1063/1.2807659}, } @Book{Finkelstein96a, Title = {{Quantum Relativity: A Synthesis of the Ideas of {Einstein and Heisenberg}}}, Author = {Finkelstein, D. R.}, Publisher = {Springer}, Year = {1996}, Address = {New York}, DOI = {10.1007/978-3-642-60936-7}, ISBN = {9783540570844} } @Article{FiSaScWu96, Title = {Bifurcation from relative equilibria of noncompact group actions: {Skew} products, meanders, and drifts}, Author = {Fiedler, B. and Sandstede, B. and Scheel, A. and Wulff, C.}, Journal = {Doc. Math.}, Year = {1996}, Pages = {479--505}, Volume = {141}, URL = {http://emis.ams.org/journals/DMJDMV/vol-01/20.pdf} } @Article{Fisher67, Title = {The theory of condensation and the critical point}, Author = {Fisher, M. E.}, Journal = {Physics}, Year = {1967}, Pages = {255--283}, Volume = {3}, URL = {http://inspirehep.net/record/1304501/files/vol3p255-283_001.pdf} } @Article{FiTu98, Title = {Normal forms, resonances, and meandering tip motions near relative equilibria of {Euclidean} group actions}, Author = {Fiedler, B. and Turaev, D.}, Journal = {Arch. Rational Mech. Anal.}, Year = {1998}, Pages = {129--159}, Volume = {145}, DOI = {10.1007/s002050050126} } @Article{FJolly95, author = {C. Foias and M. S. Jolly}, title = {On the numerical algebraic approximation of global attractors}, journal = {Nonlinearity}, year = {1995}, volume = {8}, pages = {295--319}, doi = {10.1088/0951-7715/8/3/001}, } @Article{FJS63, Title = {Quaternionic representations of compact groups}, Author = {Finkelstein, D. and Jauch, J. M. and Speiser, D.}, Journal = {J. Math. Phys.}, Year = {1963}, Pages = {136--140}, Volume = {4}, DOI = {10.1063/1.1703880} } @Article{FJSS62, Title = {Foundations of quaternion quantum mechanics}, Author = {Finkelstein, D. and Jauch, J. M. and Schiminovich, S. and Speiser, D.}, Journal = {J. Math. Phys.}, Year = {1962}, Pages = {207--220}, Volume = {3}, DOI = {10.1063/1.1703794} } @Article{FJSS63, Title = {Principle of general {Q} covariance}, Author = {Finkelstein, D. and Jauch, J. M. and Schiminovich, S. and Speiser, D.}, Journal = {J. Math. Phys.}, Year = {1963}, Pages = {788--796}, Volume = {4}, DOI = {10.1063/1.1724320} } @Article{FKYY83, Title = {The {Liapunov} dimension of strange attractors}, Author = {P. Frederickson and J. L. Kaplan and E. D. Yorke and J. A. Yorke}, Journal = {J. Diff. Eqn.}, Year = {1983}, Pages = {185--207}, Volume = {49}, DOI = {10.1016/0022-0396(83)90011-6} } @Article{Fl89, author = {Flessas, G. P.}, title = {New exact-solutions of the complex {Lorenz} equations}, journal = {J. Phys. A}, year = {1989}, volume = {22}, pages = {L137--L141}, doi = {10.1088/0305-4470/22/5/001}, } @Article{fl92, author = {C. Falcolini and R. de la Llave}, title = {Numerical calculation of domains of analyticity for perturbation theories in the presence of small divisors}, journal = {J. Stat. Phys.}, year = {1992}, volume = {67}, pages = {645--666}, doi = {10.1007/bf01049723}, } @Article{FlLe91, author = {Flessas, G. P. and Leach, P. G. L.}, title = {A completely integrable case in the complex {Lorenz} equations}, journal = {Phys. Lett. A}, year = {1991}, volume = {154}, pages = {127--130}, doi = {10.1016/0375-9601(91)90749-x}, } @Article{Floquet1883, author = {Floquet, G.}, title = {Sur les {\'e}quations diff{\'e}rentielles lin{\'e}aires \`a coefficients p{\'e}riodiques}, journal = {Ann. Sci. Ec. Norm. Sup.}, year = {1883}, volume = {12}, pages = {47--88}, url = {http://www.numdam.org/item?id=ASENS_1883_2_12__47_0}, } @Article{FNSTks85, author = {C. Foias and B. Nicolaenko and G. R. Sell and R. T{\'e}mam}, title = {Inertial manifold for the {Kuramoto-Sivashinsky} equation}, journal = {C. R. Acad. Sci., Paris}, year = {1985}, volume = {301}, pages = {285--288}, url = {http://gallica.bnf.fr/ark:/12148/bpt6k6446253z/f299}, } @Article{FNSTks88, author = {C. Foias and B. Nicolaenko and G. R. Sell and R. T{\'e}mam}, title = {Inertial manifolds for the {Kuramoto-Sivashinsky} equation and an estimate of their lowest dimension}, journal = {J. Math. Pure Appl.}, year = {1988}, volume = {67}, pages = {197--226}, url = {http://purl.umn.edu/4494}, } @Article{Foias1988a, author = {Foias, C. and Sell, G. R. and T{\'e}mam, R.}, title = {Inertial manifolds for nonlinear evolutionary equations}, journal = {J. Diff. Eqn.}, year = {1988}, volume = {73}, pages = {309--353}, doi = {10.1016/0022-0396(88)90110-6}, } @Book{foias2001, author = {Foias, C. and Manley, O. and Rosa, R. and T{\'e}mam, R.}, publisher = {Cambridge Univ. Press}, title = {{{Navier--Stokes} Equations and Turbulence}}, year = {2001}, address = {Cambridge UK}, doi = {10.1017/cbo9780511546754}, } @Article{foias88, Title = {On the computation of inertial manifolds}, Author = {C. Foias and M. S. Jolly and I. G. Kevrekidis and G. R. Sell and E. S. Titi}, Journal = {Phys. Lett. A}, Year = {1988}, Pages = {433--436}, Volume = {131}, DOI = {10.1016/0375-9601(88)90295-2} } @Article{FoMcGui84, author = {Fowler , A. C. and McGuinness, M. J.}, title = {On the nature of the torus in the complex {Lorenz} equations}, journal = {SIAM J. Appl. Math.}, year = {1984}, volume = {44}, pages = {681--700}, doi = {10.1137/0144049}, } @Article{ForKol75, Title = {Complex zeros of the {Jonqui{\`e}re} or polylogarithm function}, Author = {B. Fornberg and K. S. K{\"o}lbig}, Journal = {Math. Comp.}, Year = {1975}, Pages = {582--599}, Volume = {29}, DOI = {10.1090/S0025-5718-1975-0369278-0} } @Article{Forrester13, author = {Forrester, P. J.}, title = {Lyapunov exponents for products of complex {Gaussian} random matrices}, journal = {J. Stat. Phys.}, year = {2013}, volume = {151}, pages = {796--808}, doi = {10.1007/s10955-013-0735-7}, } @Article{fou, Title = {Bifurcations of a quadratic two-dimensional diffeomorphism, homoclinic and heteroclinic situations}, Author = {D. Fournier and H. Kawakami and C. Mira}, Journal = {C. R. Acad. Sci., Paris}, Year = {1984}, Pages = {253--256}, Volume = {298}, URL = {http://gallica.bnf.fr/ark:/12148/bpt6k5493988t/f23.item} } @Article{FouBik10, Title = {Riding a spiral wave: Numerical simulation of spiral waves in a comoving frame of reference}, Author = {A. J. Foulkes and V. N. Biktashev}, Journal = {Phys. Rev. E}, Year = {2010}, Pages = {046702}, Volume = {81}, DOI = {10.1103/PhysRevE.81.046702} } @PhdThesis{Foulkes09thesis, author = {A. J. Foulkes}, school = {Univ. of Liverpool}, title = {{Drift and Meander of Spiral Waves}}, year = {2020}, address = {Liverpool, UK}, doi = {10.17638/03069622}, } @Article{FowlerCLE82, author = {Fowler , A. C. and {Gibbon}, J. D. and {McGuinness}, M. J.}, title = {The complex {Lorenz} equations}, journal = {Physica D}, year = {1982}, volume = {4}, pages = {139--163}, doi = {10.1016/0167-2789(82)90057-4}, } @Article{FowlerCLE83, author = {Fowler , A. C. and Gibbon, J. D. and McGuinness, M. J.}, title = {The real and complex {Lorenz} equations and their relevance to physical systems}, journal = {Physica D}, year = {1983}, volume = {7}, pages = {139--163}, doi = {10.1016/0167-2789(83)90123-9}, } @Article{fpt, author = {M. J. Feigenbaum and I. Procaccia and T. T{\'e}l}, title = {Scaling properties of multifractals as an eigenvalue problem}, journal = {Phys. Rev. A}, year = {1989}, volume = {39}, pages = {5359--5372}, doi = {10.1103/PhysRevA.39.5359}, } @Article{FR06, Title = {{Ruelle--Pollicott} resonances for real analytic hyperbolic maps}, Author = {F. Faure and N. Roy}, Journal = {Nonlinearity}, Year = {2006}, Pages = {123--1252}, Volume = {19}, DOI = {10.1088/0951-7715/19/6/002} } @Article{FR81, Title = {Stable and unstable manifolds of the {H{\'e}non} mapping}, Author = {V. Franceschini and L. Russo}, Journal = {J. Stat. Phys.}, Year = {1981}, Pages = {757}, Volume = {25}, DOI = {10.1007/BF01022365} } @Article{Frank1898, author = {W. S. Franklin}, journal = {Phys. Rev.}, title = {New books}, year = {1898}, pages = {173--174}, volume = {6}, doi = {10.1103/PhysRevSeriesI.6.170}, url = {http://ChaosBook.org/extras/grasshoppereffect.html}, } @Article{Franks90, author = {J. Franks}, title = {Periodic points and rotation numbers for area-preserving diffeomorphisms of the plane}, journal = {Publ. Math. IHES}, year = {1990}, volume = {71}, pages = {105--120}, url = {http://archive.numdam.org/ARCHIVE/PMIHES/PMIHES_1990__71_/PMIHES_1990__71__105_0/PMIHES_1990__71__105_0.pdf} } @Article{FrCv11, Title = {Reduction of continuous symmetries of chaotic flows by the method of slices}, Author = {Froehlich, S. and Cvitanovi{\'c}, P.}, Journal = {Commun. Nonlinear Sci. Numer. Simul.}, Year = {2012}, Pages = {2074--2084}, Volume = {17}, DOI = {10.1016/j.cnsns.2011.07.007} } @Article{FredDet, author = {Cvitanovi{\'c}, P. and Rosenqvist, P. E. and Vattay, G. and Rugh, H. H.}, journal = {Chaos}, title = {A {Fredholm} determinant for semiclassical quantization}, year = {1993}, pages = {619--636}, volume = {3}, doi = {10.1063/1.165992}, } @MastersThesis{freddy, author = {F. Christiansen}, title = {{Analysis of Chaotic Dynamical Systems in Terms of Cycles}}, school = {Univ. of Copenhagen}, year = {1989}, address = {Copenhagen}, } @PhdThesis{FreddyThesis, author = {Christiansen, F.}, title = {{Periodic Orbits in Classical and Quantum Chaos}}, school = {Copenhagen Univ.}, year = {1992}, address = {Copenhagen}, } @Article{freire_limit_2007, author = {E. Freire}, title = {Limit cycles and {Lie} symmetries}, journal = {Bull. Sci. math.}, year = {2007}, volume = {131}, pages = {501--517}, doi = {10.1016/j.bulsci.2006.03.015}, } @Incollection{fri2, author = {D. Fried}, title = {Lefschetz formula for flows}, booktitle = {{The Lefschetz Centennial Conference}}, publisher = {Amer. Math. Soc.}, year = {1987}, editor = {Gitler, S.}, volume = {58}, isbn = {9780821850633}, pages = {19--69}, doi = {10.1090/conm/058.3/893856}, } @Article{frie, author = {D. Fried}, title = {The {Zeta} functions of {Ruelle} and {Selberg I}}, journal = {Ann. Scient. Ec. Norm. Sup.}, year = {1986}, volume = {19}, pages = {491}, url = {http://www.numdam.org/item?id=ASENS_1986_4_19_4_491_0}, } @Article{Fried95, author = {D. Fried}, title = {Meromorphic zeta functions for analytic flows}, journal = {Commun. Math. Phys.}, year = {1995}, volume = {174}, pages = {161--190}, doi = {10.1007/bf02099469}, } @Article{FriedmanDoedelConnections91, author = {Friedman, M. J. and Doedel, E. J.}, title = {Numerical computation of invariant manifolds connecting fixed points}, journal = {SIAM J. Numer. Anal.}, year = {1991}, volume = {28}, pages = {789--808}, doi = {10.1137/0728042}, } @Article{Frigo05, author = {M. Frigo and S. G. Johnson}, journal = {Proc. IEEE}, title = {The design and implementation of {FFTW3}}, year = {2005}, pages = {216--231}, volume = {93}, doi = {10.1109/jproc.2004.840301}, } @Book{frisch, author = {U. Frisch}, publisher = {Cambridge Univ. Press}, title = {{Turbulence: The Legacy of A. N. Kolmogorov}}, year = {1996}, address = {Cambridge UK}, doi = {10.1063/1.881555}, } @Article{frisch86, author = {U. Frisch and B. Hasslacher and Y. Pomeau}, title = {Lattice-gas automata for the {Navier-Stokes} equation}, journal = {Phys. Rev. Lett.}, year = {1986}, volume = {56}, pages = {1505--1508}, doi = {10.1103/physrevlett.56.1505}, } @Article{frisch87, author = {U. Frisch and Z. S. She and P.-L. Sulem}, title = {Large-scale flow driven by the anisotropic kinetic alpha effect}, journal = {Physica D}, year = {1987}, volume = {28}, pages = {382--392}, doi = {10.1142/9789814434348_0044}, } @Article{FrKhaMa03, author = {Frisch, U. and Khanin, K. and Matsumoto, T.}, title = {Multifractality of the {Feigenbaum} attractor and fractional derivatives}, journal = {J. Stat. Phys.}, year = {2005}, volume = {121}, pages = {671--695}, doi = {10.1007/s10955-005-7011-4}, } @Book{Fro92, title = {{Introduction to Chaos and Coherence}}, publisher = {Taylor \& Francis}, year = {1992}, author = {Fr{\o}yland, J.}, isbn = {9780750301954}, address = {Bristol}, } @Techreport{Froeh10, Title = {Reducing continuous symmetries with linear slice}, Author = {Froehlich, S.}, Institution = {Georgia Inst. of Technology}, Year = {2010}, Publisher = {Center for Nonlinear Science}, URL = {http://ChaosBook.org/projects} } @Article{Froy07a, author = {G. Froyland}, title = {On {Ulam} approximation of the isolated spectrum and eigenfunctions of hyperbolic maps}, journal = {Discrete Contin. Dyn. Syst.}, year = {2007}, volume = {17}, pages = {671--689}, doi = {10.3934/dcds.2007.17.671}, } @Article{Froy-1, author = {G. Froyland}, title = {Computer-assisted bounds for the rate of decay of correlations}, journal = {Commun. Math. Phys.}, year = {1997}, volume = {189}, pages = {237--257}, doi = {10.1007/s002200050198}, } @InProceedings{Froy-2, author = {G. Froyland}, title = {Extracting dynamical behaviour via {Markov} models}, booktitle = {{Nonlinear Dynamics and Statistics: Proc. Newton Institute, Cambridge 1998}}, year = {2001}, editor = {A. Mees}, pages = {281--321}, address = {Boston}, publisher = {Birkh\"auser}, doi = {10.1007/978-1-4612-0177-9_12}, isbn = {978-1-4612-6648-8}, } @Article{Froy99, author = {Froyland, G.}, title = {Using {Ulam}'s method to calculate entropy and other dynamical invariants}, journal = {Nonlinearity}, year = {1999}, volume = {12}, pages = {79--101}, doi = {10.1088/0951-7715/12/1/006}, } @Article{froyland_alfsen, author = {Fr{\o}yland, J. and Alfsen, K. H.}, title = {{Lyapunov}-exponent spectra for the {Lorenz} model}, journal = {Phys. Rev. A}, year = {1984}, volume = {29}, pages = {2928}, doi = {10.1103/physreva.29.2928}, } @Article{FSTks86, author = {U. Frisch and Z. S. She and O. Thual}, title = {Viscoelastic behavior of cellular solutions to the {Kuramoto-Sivashinsky} model}, journal = {J. Fluid Mech.}, year = {1986}, volume = {168}, pages = {221--240}, doi = {10.1017/s0022112086000356}, } @Article{FuDu98, Title = {Infinite-dimensional linear dynamical systems with chaoticity}, Author = {X. Fu and J. Duan}, Journal = {J. Nonlin. Sci.}, Year = {1999}, Volume = {9}, DOI = {10.1007/s003329900069} } @Article{Fuj83, Title = {Statistical dynamics generated by fluctuations of local {Lyapunov} exponents}, Author = {Fujisaka, H.}, Journal = {Progr. Theor. Phys.}, Year = {1983}, Pages = {1264--1275}, Volume = {70}, DOI = {10.1143/PTP.70.1264} } @Article{Fujisaka01101982, Title = {Multiperiodic flows, chaos and {Lyapunov} exponents}, Author = {Fujisaka, H.}, Journal = {Progr. Theor. Phys.}, Year = {1982}, Pages = {1105--1121}, Volume = {68}, DOI = {10.1143/PTP.68.1105} } @Article{FuKr97, author = {M. Fulmek and C. Krattenthaler}, title = {Lattice path proofs for determinant formulas for symplectic and orthogonal characters}, journal = {J. Combin. Theory A}, year = {1997}, volume = {77}, pages = {3--50}, doi = {10.1006/jcta.1996.2711}, url = {http://www.mat.univie.ac.at/~kratt/artikel/symporth.html}, } @Book{Fulton91, title = {{Representation Theory}}, publisher = {Springer}, year = {1991}, author = {W. Fulton and J. Harris}, isbn = {9781461209799}, address = {New York}, doi = {10.1007/978-1-4612-0979-9}, } @Article{funceq2, Title = {The universal metric properties of nonlinear transformations}, Author = {M. J. Feigenbaum}, Journal = {J. Stat. Phys.}, Year = {1979}, Note = {Reprinted in \refref{cvt89b}}, Pages = {669--706}, Volume = {21}, DOI = {10.1007/BF01107909} } @Misc{Feigenbaum76, author = {M. J. Feigenbaum}, title = {Universality in complex discrete dynamics}, howpublished = {{Los Alamos Theoretical Division Annual Report 1975-1976}}, year = {1976}, pages = {98--102}, url = {http://ChaosBook.org/extras/mjf/LA-6816-PR.pdf}, } @Article{G00, author = {S. Grossmann}, title = {The onset of shear turbulence}, journal = {Rev. Mod. Phys.}, year = {2000}, volume = {72}, pages = {603--618}, doi = {10.1103/RevModPhys.72.603}, } @Article{GA, Title = {Ruelle classical resonances and dynamical chaos: {The} three- and four-disk scatterers}, Author = {P. Gaspard and D. Alonso}, Journal = {Phys. Rev. A}, Year = {1992}, Pages = {8383}, Volume = {45}, DOI = {10.1103/PhysRevA.45.8383} } @Article{ga2, Title = {Diffusion in uniformly hyperbolic one-dimensional maps and {Appell} polynomials}, Author = {P. Gaspard}, Journal = {Phys. Lett. A}, Year = {1992}, Pages = {13--17}, Volume = {168}, DOI = {10.1016/0375-9601(92)90321-C} } @Inproceedings{GaBaMaHo92, author = {Gaspard, P. and Baras, F. and Mareschal, M. and Holian, B.}, title = {Dynamical chaos underlying diffusion in the {Lorentz} gas}, booktitle = {{Microscopic simulations of complex hydrodynamic phenomena: {Proceedings} of {ASI}}}, year = {1992}, pages = {301--322}, address = {New York}, publisher = {Plenum}, doi = {10.1007/978-1-4899-2314-1_22}, } @Article{galan_stability_2002, Title = {Stability and bifurcations of the figure-8~{s}olution of the three-body problem}, Author = {Gal{\'a}n, J. and Mu{\~n}oz-Almaraz, F. J. and Freire, E. and Doedel, E. J. and Vanderbauwhede, A.}, Journal = {Phys. Rev. Lett.}, Year = {2002}, Pages = {241101}, Volume = {88}, DOI = {10.1103/PhysRevLett.88.241101} } @Article{GaliTuck14, Title = {On the structure of existence regions for sinks of the {H{\'e}non} map}, Author = {Galias, Z. and Tucker, W.}, Journal = {Chaos}, Year = {2014}, Pages = {013120}, Volume = {24}, DOI = {10.1063/1.4865110} } @Article{gallas_counting, author = {J. A. C. Gallas}, title = {Counting orbits in conjugacy classes of the {H{\'e}non Hamiltonian} repeller}, journal = {Phys. Lett. A}, year = {2007}, volume = {360}, pages = {512--514}, doi = {10.1016/j.physleta.2006.08.065} } @Incollection{Gallavotti75, author = {Gallavotti, G.}, title = {Lectures on the billiard}, booktitle = {{Dynamical Systems, Theory and Applications}}, publisher = {Springer}, year = {1975}, editor = {Moser, J.}, volume = {38}, isbn = {978-3-540-07171-6}, series = {Lecture Notes in Physics}, pages = {236--295}, address = {Berlin}, doi = {10.1007/3-540-07171-7_7}, } @Article{Gallavotti76, Title = {Funzioni zeta ed insiemi basilari}, Author = {Gallavotti, G.}, Journal = {Accad. Lincei. Rend. Sc. Fis. Mat. e Nat}, Year = {1976}, Pages = {309--317}, Volume = {61} } @Article{GamLes16, author = {Gameiro, M. and Lessard, J. P.}, journal = {SIAM J. Appl. Dyn. Syst.}, title = {A posteriori verification of invariant objects of evolution equations: periodic orbits in the {Kuramoto-Sivashinsky PDE}}, year = {2017}, pages = {687--728}, volume = {16}, doi = {10.1137/16m1073789}, } @Book{GaQu95, title = {{{Lyapunov} Matrix Equation in System Stability and Control}}, publisher = {Academic}, year = {1995}, author = {Z. Gaji{\'c} and M. Qureshi}, address = {New York}, } @Article{garcia_geometrical_1996, author = {R Garcia}, title = {Geometrical conditions for the stability of orbits in planar systems}, journal = {Math. Proc. Cambridge Philos. Soc.}, year = {1996}, volume = {120}, pages = {499--520}, doi = {10.1017/s0305004100075046}, } @Article{Garcia2011, author = {Garcia, S.P. and Pinho, A.J.}, title = {Minimal absent words in four human genome assemblies}, journal = {PLoS One}, year = {2011}, volume = {6}, doi = {10.1371/journal.pone.0029344}, } @Article{garnier, author = {N. Garnier and A. Chiffaudel and F. Daviaud and A. Prigent}, title = {Nonlinear dynamics of waves and modulated waves in 1{D} thermocapillary flows}, journal = {Physica D}, year = {2003}, volume = {174}, pages = {1--29}, doi = {10.1016/S0167-2789(02)00680-2}, } @Article{GarSar04, author = {Garc\'{i}a-Mata, I. and Saraceno, M.}, title = {Spectral properties and classical decays in quantum open systems}, journal = {Phys. Rev. E}, year = {2004}, volume = {69}, pages = {056211}, doi = {10.1103/PhysRevE.69.056211}, } @Article{GasBar95, Title = {Chaotic scattering and diffusion in the {Lorentz} gas}, Author = {Gaspard, P. and Baras, F.}, Journal = {Phys. Rev. E}, Year = {1995}, Pages = {5332--5352}, Volume = {51}, DOI = {10.1103/PhysRevE.51.5332} } @Article{GasNic90, Title = {Transport properties, {Lyapunov} exponents, and entropy per unit time}, Author = {Gaspard, P. and Nicolis, G.}, Journal = {Phys. Rev. Lett.}, Year = {1990}, Pages = {1693--1696}, Volume = {65}, DOI = {10.1103/PhysRevLett.65.1693} } @Article{gasp02, author = {P. Gaspard}, title = {Trace formula for noisy flows}, journal = {J. Stat. Phys.}, year = {2002}, volume = {106}, pages = {57}, doi = {10.1023/A:1013167928166} } @Article{gasp95, Title = {Spectral signature of the pitchfork bifurcation: {Liouville} equation approach}, Author = {Gaspard, P. and Nicolis, G. and Provata, A. and Tasaki, S.}, Journal = {Phys. Rev. E}, Year = {1995}, Pages = {74--94}, Volume = {51}, DOI = {10.1103/PhysRevE.51.74} } @Article{Gaspard92, Title = {Diffusion, effusion, and chaotic scattering: {An} exactly solvable {Liouvillian} dynamics}, Author = {Gaspard, P.}, Journal = {J. Stat. Phys.}, Year = {1992}, Pages = {673--747}, Volume = {68}, DOI = {10.1007/BF01048873} } @Inbook{Gaspard92a, Title = {From dynamical chaos to diffusion}, Author = {Gaspard, P.}, Editor = {Gy{\"o}rgyi, G. and Kondor, I. and Sasv{\'a}ri, L. and T{\'e}l, T.}, Pages = {322--334}, Publisher = {World Scientific}, Year = {1992}, Address = {Singapore}, Booktitle = {{From Phase Transitions to Chaos: Topics in Modern Statistical Physics}}, DOI = {10.1142/9789814355872_0026} } @Article{GaspRice89a, Title = {Scattering from a classically chaotic repellor}, Author = {P. Gaspard and S. A. Rice}, Journal = {J. Chem. Phys.}, Year = {1989}, Pages = {2225--2241}, Volume = {90}, DOI = {10.1063/1.456017} } @Article{GaspRice89b, Title = {Semiclassical quantization of the scattering from a classically chaotic repellor}, Author = {P. Gaspard and S. A. Rice}, Journal = {J. Chem. Phys.}, Year = {1989}, Pages = {2242--2254}, Volume = {90}, DOI = {10.1063/1.456018} } @Article{GaspRice89c, Title = {Exact quantization of the scattering from a classically chaotic repellor}, Author = {P. Gaspard and S. A. Rice}, Journal = {J. Chem. Phys.}, Year = {1989}, Pages = {2255--2262}, Volume = {90}, DOI = {10.1063/1.456019} } @Article{gasull_stability_2008, author = {A. Gasull and H. Giacomini and M. Grau}, title = {On the stability of periodic orbits for differential systems in {\${\textbackslash} mathbb {R\textasciicircum} n\$}}, journal = {Discrete Contin. Dyn. Syst.}, year = {2008}, volume = {10}, pages = {495--509}, doi = {10.3934/dcdsb.2008.10.495}, } @Article{GasWan88, Title = {Sporadicity: {Between} periodic and chaotic dynamical behaviors}, Author = {Gaspard, P. and Wang, X.-J.}, Journal = {Proc. Natl. Acad. Sci. USA}, Year = {1988}, Pages = {4591--4595}, Volume = {85}, URL = {http://www.pnas.org/content/85/13/4591.abstract} } @Book{gatermannHab, title = {{Computer Algebra Methods for Equivariant Dynamical Systems}}, publisher = {Springer}, year = {2000}, author = {Gatermann, K.}, isbn = {9783540671619}, address = {New York}, doi = {10.1007/bfb0104059}, } @Book{gauge, title = {{Chaos and Gauge Field Theory}}, publisher = {World Scientific}, year = {1994}, author = {T. S. Bir\'{o} and S. G. Matinyan and B. M{\"u}ller}, isbn = {978-981-02-2079-2}, address = {Singapore}, } @Article{GaXiLa11, author = {Gao, A. and Xie, J. and Lan, Y.}, title = {Accelerating cycle expansions by dynamical conjugacy}, journal = {J. Stat. Phys.}, year = {2012}, volume = {146}, pages = {56--66}, doi = {10.1007/s10955-011-0369-6}, } @InProceedings{GB92, Title = {Dynamical chaos underlying diffusion in the {Lorentz} gas}, Author = {P. Gaspard and F. Baras}, Booktitle = {Microscopic Simulations of Complex Hydrodynamic Phenomena}, Year = {1992}, Address = {New York}, Editor = {M. Mareschal and B. L. Holian}, Pages = {301--322}, Publisher = {Plenum}, Chapter = {Microscopic simulations of complex hydrodynamic phenomena}, DOI = {10.1007/978-1-4899-2314-1_22}, ISBN = {9781489923141} } @Article{GBHMRV10, author = {Gay-Balmaz, F. and Holm, D. D. and {Meier}, D. M. and Ratiu, T. S. and {Vialard}, {F.-X.}}, title = {Invariant higher-order variational problems}, journal = {Commun. Math. Phys.}, year = {2011}, volume = {309}, pages = {413--458}, doi = {10.1007/s00220-011-1313-y}, } @Article{GBRS07, Title = {The effect of pitchfork bifurcations on the spectral statistics of {Hamiltonian} systems}, Author = {M. Guti{\'e}rrez and M. Brack and K. Richter and A. Sugita}, Journal = {J. Phys. A.}, Year = {2007}, Pages = {1525}, Volume = {40}, DOI = {10.1088/1751-8113/40/7/007} } @Article{GeiNie81, Title = {Universal fine structure of the chaotic region in period-doubling systems}, Author = {Geisel, T and Nierwetberg, J}, Journal = {Phys. Rev. Lett.}, Year = {1981}, Pages = {975}, Volume = {47}, DOI = {10.1103/PhysRevLett.47.975} } @Article{GeiNiZa, author = {Zacherl, A. and Geisel, T. and Nierwetberg, J. and Radons, G.}, journal = {Phys. Lett. A}, title = {Power spectra for anomalous diffusion in the extended {Sinai} billiard}, year = {1986}, pages = {317--321}, volume = {114}, doi = {10.1016/0375-9601(86)90568-2}, } @Article{GeiTho, Title = {Anomalous diffusion in intermittent chaotic systems}, Author = {Geisel, T. and Thomae, S.}, Journal = {Phys. Rev. Lett.}, Year = {1984}, Pages = {1936}, Volume = {52}, DOI = {10.1103/PhysRevLett.52.1936} } @Book{Gelfand61, title = {{Lectures on Linear Algebra}}, publisher = {Dover}, year = {1961}, author = {I. M. Gel'fand}, isbn = {0486660826}, address = {New York}, } @Book{Gell-Mann61, title = {{The Eightfold Way: A Theory of Strong Interaction Symmetry}}, publisher = {CalTech}, year = {1961}, author = {Gell-Mann, M.}, doi = {10.2172/4008239}, } @Article{Gell-Mann62, Title = {Symmetries of baryons and mesons}, Author = {Gell-Mann, M.}, Journal = {Phys. Rev.}, Year = {1962}, Pages = {1067--1084}, Volume = {125}, DOI = {10.1103/PhysRev.125.1067} } @Article{GeMaWu10, Title = {Semiclassical quantization of the diamagnetic hydrogen atom with near-action-degenerate periodic-orbit bunches}, Author = {Gehrke, J. and Main, J. and Wunner, G.}, Journal = {Phys. Rev. E}, Year = {2010}, Pages = {066207}, Volume = {82}, DOI = {10.1103/PhysRevE.82.066207} } @Book{Georgi99, title = {{Lie Algebras in Particle Physics}}, publisher = {Perseus Books}, year = {1999}, author = {H. Georgi}, isbn = {9780813346113}, address = {Reading, MA}, doi = {10.1119/1.12947}, } @Article{GeZe84, Title = {Models of representations of classical groups and their hidden symmetries}, Author = {Gel'fand, I. M. and Zelevinskii, A. V.}, Journal = {Funct. Anal. Appl.}, Year = {1984}, Pages = {183--198}, Volume = {18}, DOI = {10.1007/BF01086156} } @Article{GG93, Title = {Billiards correlation functions}, Author = {Garrido, P. L. and Gallavotti, G.}, Journal = {J. Stat. Phys.}, Year = {1994}, Pages = {549--585}, Volume = {76}, DOI = {10.1007/BF02188675} } @Article{GGJLF10, author = {R. Gilmore and J.-M. Ginoux and T. Jones and C. Letellier and U. S. Freitas}, title = {Connecting curves for dynamical systems}, journal = {J. Phys. A}, year = {2010}, volume = {43}, pages = {255101}, doi = {10.1088/1751-8113/43/25/255101}, } @Article{GHCV08, author = {Halcrow, J. and Gibson, J. F. and Cvitanovi{\'c}, P. and Viswanath, D.}, title = {Heteroclinic connections in plane {Couette} flow}, journal = {J. Fluid Mech.}, year = {2009}, volume = {621}, pages = {365--376}, doi = {10.1017/S0022112008005065}, } @Article{GHCW07, Title = {Visualizing the geometry of state-space in plane {Couette} flow}, Author = {J. F. Gibson and J. Halcrow and P. Cvitanovi{\'c}}, Journal = {J. Fluid Mech.}, Year = {2008}, Pages = {107--130}, Volume = {611}, DOI = {10.1017/S002211200800267X} } @Article{GiacoOtto05, Title = {New bounds for the {Kuramoto-Sivashinsky} equation}, Author = {L. Giacomelli and F. Otto}, Journal = {Commun. Pure Appl. Math.}, Year = {2005}, Pages = {297--318}, Volume = {58}, URL = {http://www-mathphys.iam.uni-bonn.de/~otto/web/main-en.htm} } @Article{GiaUll90-1, author = {M.-J. Giannoni and D. Ullmo}, title = {Coding chaotic billiards: {I. Non-compact} billiards on a negative curvature manifold}, journal = {Physica D.}, year = {1990}, volume = {41}, pages = {371--390}, doi = {10.1016/0167-2789(90)90005-A}, } @Article{GiaUll95-2, author = {D. Ullmo and M.-J. Giannoni}, title = {Coding chaotic billiards: {II. Compact} billiards defined on the pseudosphere}, journal = {Physica D.}, year = {1995}, volume = {84}, pages = {329--356}, doi = {10.1016/0167-2789(90)90005-A}, } @Article{GibMcCLE82, author = {Gibbon, J. D. and McGuinness, M. J.}, title = {The real and complex {Lorenz} equations in rotating fluids and lasers}, journal = {Physica D}, year = {1982}, volume = {5}, pages = {108--122}, doi = {10.1016/0167-2789(82)90053-7}, } @Article{GibMcCLE83, author = {Gibbon, J. D. and McGuinness, M. J.}, title = {The real and complex {Lorenz} equations}, journal = {Proc. R. Irish. Acad. A}, year = {1983}, volume = {83}, pages = {17--22}, url = {http://www.jstor.org/stable/20489162}, } @Book{GiBo, author = {G. Casati and B. V. Chirikov}, publisher = {Cambridge Univ. Press}, title = {{Quantum Chaos: Between Order and Disorder}}, year = {1995}, address = {Cambridge UK}, doi = {10.1017/cbo9780511599989}, } @Techreport{GibsonMovies, Title = {Movies of plane {Couette}}, Author = {J. F. Gibson and P. Cvitanovi{\'c}}, Institution = {Georgia Inst. of Technology}, Year = {2011}, Publisher = {Center for Nonlinear Science}, URL = {http://ChaosBook.org/tutorials} } @Phdthesis{GibsonPhD, Title = {{Dynamical-systems Models of Wall-bounded, Shear-flow Turbulence}}, Author = {J. F. Gibson}, School = {Cornell Univ.}, Year = {2002} } @Article{GiChLiPo12, Title = {Covariant {Lyapunov} vectors}, Author = {Ginelli, F. and Chat\'{e}, H. and Livi, R. and Politi, A.}, Journal = {J. Phys. A}, Year = {2013}, Pages = {254005}, Volume = {46}, DOI = {10.1088/1751-8113/46/25/254005} } @Article{GiKaChPoAl11, Title = {Chaos in the {Hamiltonian} mean-field model}, Author = {Ginelli, F. and Takeuchi, K. A. and Chat{\'e}, H. and Politi, A. and Torcini A.}, Journal = {Phys. Rev. E}, Year = {2011}, Pages = {066211}, Volume = {84}, DOI = {10.1103/PhysRevE.84.066211} } @Article{Gilbert02, Title = {Advected fields in maps: {I. Magnetic} flux growth in the stretch--fold--shear map}, Author = {A. D. Gilbert}, Journal = {Physica D}, Year = {2002}, Pages = {167--196}, Volume = {166}, DOI = {10.1016/S0167-2789(02)00444-X} } @InBook{Gilbert2003, author = {Gilbert, A. D.}, chapter = {Dynamo theory}, pages = {355--441}, publisher = {Elsevier}, title = {{Handbook of Mathematical Fluid Dynamics}}, year = {2003}, volume = {2}, } @Article{GilbLef08, Title = {Heat conductivity from molecular chaos hypothesis in locally confined billiard systems}, Author = {Gilbert, T. and Lefevere, R.}, Journal = {Phys. Rev. Lett.}, Year = {2008}, Pages = {200601}, Volume = {101}, DOI = {10.1103/PhysRevLett.101.200601} } @Book{gilmore74, title = {{Lie Groups, {Lie} Algebras, and some of their Applications}}, publisher = {Dover}, year = {1974}, author = {R. Gilmore}, isbn = {9780486445298}, address = {New York}, doi = {10.1063/1.3128987}, } @Article{GilRio61, Title = {Symmetry types of periodic sequences}, Author = {Gilbert, E. N. and Riordan, J.}, Journal = {Illinois J. Math.}, Year = {1961}, Pages = {657--665}, Volume = {5}, URL = {http://projecteuclid.org/euclid.ijm/1255631587} } @Article{GilSan09, Title = {Persistence effects in deterministic diffusion}, Author = {Gilbert, T. and Sanders, D. P.}, Journal = {Phys. Rev. E}, Year = {2009}, Pages = {041121}, Volume = {80}, DOI = {10.1103/PhysRevE.80.041121} } @Article{ginelli-2007-99, author = {Ginelli, F. and Poggi, P. and Turchi, A. and Chat{\'e}, H. and Livi, R. and Politi, A.}, journal = {Phys. Rev. Lett.}, title = {Characterizing dynamics with covariant {Lyapunov} vectors}, year = {2007}, pages = {130601}, volume = {99}, doi = {10.1103/PhysRevLett.99.130601}, } @Article{GioAdr98, author = {M. Giona and A. Adrover}, title = {Nonuniform stationary measure of the invariant unstable foliation in {Hamiltonian} and fluid mixing systems}, journal = {Phys. Rev. Lett.}, year = {1998}, volume = {81}, pages = {3864}, doi = {10.1103/physrevlett.81.3864}, } @Article{GiPo91, Title = {Homoclinic tangencies, generating partitions and curvature of invariant manifolds}, Author = {F. Giovannini and A. Politi}, Journal = {J. Phys. A}, Year = {1991}, Pages = {1837--1848}, Volume = {24}, DOI = {10.1016/j.physd.2006.09.032}, URL = {http://www.fi.isc.cnr.it/users/antonio.politi/Reprints/056.pdf} } @Article{GIRST, author = {Z. Gills and C. Iwata, R. Roy, I. B. Scwartz and I. Triandaf}, title = {Tracking unstable steady states: {Extending} the stability regime of a multimode laser system}, journal = {Phys. Rev. Lett.}, year = {1992}, volume = {69}, pages = {3169}, doi = {10.1103/PhysRevLett.69.3169} } @Article{GJP, Title = {Universal strange attractors on wrinkled tori}, Author = {G. Gunaratne and M. H. Jensen and I. Procaccia}, Journal = {Nonlinearity}, Year = {1988}, Pages = {157--180}, Volume = {1}, DOI = {10.1088/0951-7715/1/1/006} } @Article{GK85, Title = {Generating partitions for the dissipative {H{\'e}non} map}, Author = {P. Grassberger and H. Kantz}, Journal = {Phys. Lett. A}, Year = {1985}, Pages = {235--238}, Volume = {113}, DOI = {10.1016/0375-9601(85)90016-7} } @Article{GKOS15, author = {J. Guckenheimer and B. Krauskopf and H. M. Osinga and B. Sandstede}, title = {Invariant manifolds and global bifurcations}, journal = {Chaos}, year = {2015}, volume = {25}, doi = {10.1063/1.4915528}, url = {http://www.dam.brown.edu/people/sandsted/publications/gkos-survey.pdf}, } @Article{Glanz94, Title = {Do chaos-control techniques offer hope for epilepsy?}, Author = {J. Glanz}, Journal = {Science}, Year = {1994}, Pages = {1174}, Volume = {265}, DOI = {10.1126/science.8066457} } @Article{Glanz97, Title = {Mastering the nonlinear brain}, Author = {Glanz, J.}, Journal = {Science}, Year = {1997}, Pages = {1758--1760}, Volume = {277}, DOI = {10.1126/science.277.5333.1758} } @Article{GL-Bir83a, author = {J. S. Birman and R. F. Williams}, title = {Knotted periodic orbits in dynamical systems {I: Lorenz}'s equations}, journal = {Topology}, year = {1983}, volume = {22}, pages = {47--82}, doi = {10.1016/0040-9383(83)90045-9}, } @Article{GL-Bir83b, author = {J. S. Birman and R. F. Williams}, title = {Knotted periodic orbits in dynamical systems {II: Knot} holders for fibered knots}, journal = {Contemp. Math.}, year = {1983}, volume = {20}, pages = {1--60}, doi = {10.1090/conm/020/718132}, } @Article{GLEM07, author = {{Li}, Y. and {Chevillard}, L. and {Eyink}, G. and {Meneveau}, C.}, title = {Matrix exponential-based closures for the turbulent subgrid-scale stress tensor}, journal = {Phys. Rev. E}, year = {2009}, volume = {79}, pages = {016305}, doi = {10.1103/physreve.79.016305}, } @Book{glend94, author = {Glendinning, P.}, publisher = {Cambridge Univ. Press}, title = {{Stability, Instability and Chaos: An Introduction to the Theory of Nonlinear Differential Equations}}, year = {1994}, address = {Cambridge UK}, doi = {10.1017/cbo9780511626296}, } @Book{GL-Gil02, author = {Gilmore, R. and Lefranc, M.}, publisher = {Wiley}, title = {{The Topology of Chaos}}, year = {2003}, address = {New York}, edition = {2}, isbn = {978-3-527-41067-5}, doi = {10.1002/9783527617319}, } @Article{GL-Gil07a, author = {R. Gilmore}, title = {Two-parameter families of strange attractors}, journal = {Chaos}, year = {2007}, volume = {17}, pages = {013104}, doi = {10.1063/1.2432023}, } @Book{GL-Gil07b, title = {{The Symmetry of Chaos}}, publisher = {Oxford Univ. Press}, year = {2007}, author = {R. Gilmore and C. Letellier}, isbn = {9780195310658}, address = {Oxford}, } @Article{GL-Gil98, author = {R. Gilmore}, title = {Topological analysis of chaotic dynamical systems}, journal = {Rev. Mod. Phys.}, year = {1998}, volume = {70}, pages = {1455--1529}, doi = {10.1103/RevModPhys.70.1455}, } @TechReport{GL-Jon07, author = {T. Jones}, title = {{Symmetry of Chaos Animations}}, institution = {Nonlinear Dynamics Group, Drexel Univ.}, year = {2012}, url = {http://www.physics.drexel.edu/~tim/programs/}, } @Incollection{GL-Lan87, author = {O. E. Lanford}, title = {Circle mappings}, booktitle = {{Recent Developments in Mathematical Physics}}, publisher = {Springer}, year = {1987}, editor = {H. Mitter and L. Pittner}, isbn = {978-3-642-05157-9}, pages = {1--17}, address = {Berlin}, doi = {10.1007/978-3-642-73104-4_1}, } @Article{GL-Let01, author = {C. Letellier and R. Gilmore}, title = {Covering dynamical systems: {Two}-fold covers}, journal = {Phys. Rev. E}, year = {2001}, volume = {63}, pages = {016206}, doi = {10.1103/PhysRevE.63.016206}, } @Article{GL-Let03, author = {R. Gilmore and C. Letellier}, title = {Dressed symbolic dynamics}, journal = {Phys. Rev. E}, year = {2003}, volume = {67}, pages = {036205}, doi = {10.1103/physreve.67.036205}, } @Article{GL-Let05, author = {Letellier, C. and T. Tsankov, G. Byrne and Gilmore, R.}, journal = {Phys. Rev. E}, title = {Large-scale structural reorganization of strange attractor}, year = {2005}, pages = {026212}, volume = {72}, doi = {10.1103/physreve.72.026212}, } @Article{GL-Let07, author = {C. Letellier and R. Gilmore}, title = {Symmetry groups for {$3D$} dynamical systems}, journal = {J. Phys. A}, year = {2007}, volume = {40}, pages = {5597--5620}, doi = {10.1088/1751-8113/40/21/011}, } @Article{GL-Let07a, Title = {Peeling bifurcations of toroidal chaotic attractors}, Author = {Letellier, C. and Gilmore, R. and Jones, T.}, Journal = {Phys. Rev. E}, Year = {2007}, Pages = {066204}, Volume = {76}, DOI = {10.1103/PhysRevE.76.066204} } @Article{GL-Mir93, Title = {The proto-{Lorenz} system}, Author = {R. Miranda and E. Stone}, Journal = {Phys. Lett. A}, Year = {1993}, Pages = {105--113}, Volume = {178}, DOI = {10.1016/0375-9601(93)90735-I} } @Book{GLMS01, title = {{Dynamics and Mission Design Near Libration Points: Volume I: Fundamentals: The Case of Collinear Libration Points}}, publisher = {World Scientific}, year = {2001}, author = {G{\'o}mez, G. and Llibre, J. and Mart{\'i}nez, R. and Sim{\'o}, C.}, volume = {1}, address = {Singapore}, isbn = {9789812810632}, } @Article{GloKR85, author = {R. Glowinski and H. B. Keller and L. Rheinhart}, title = {Continuation-conjugate gradient methods for the least-squares solution of nonlinear boundary value problems}, journal = {SIAM J. Sci. Statist. Comput.}, year = {1985}, volume = {6}, pages = {793--832}, doi = {10.1137/0906055}, } @Article{GL-Sha81, Title = {Strange attractors, chaotic behavior, and information flow}, Author = {R. Shaw}, Journal = {Z. Naturf. A}, Year = {1981}, Pages = {80--112}, Volume = {36}, DOI = {10.1515/zna-1981-0115} } @Article{GL-Tsa03, Title = {Strange attractors are classified by bounding tori}, Author = {T. Tsankov and R. Gilmore}, Journal = {Phys. Rev. Lett.}, Year = {2003}, Pages = {134104}, Volume = {91}, DOI = {10.1103/PhysRevLett.91.134104} } @Article{GL-Tsa04, author = {T. D. Tsankov and R. Gilmore}, title = {Topological aspects of the structure of chaotic attractors in {$\mathbb{R}^3$}}, journal = {Phys. Rev. E}, year = {2004}, volume = {69}, pages = {056206}, doi = {10.1103/PhysRevE.69.056206}, } @Article{GM00aut, author = {J. Guckenheimer and B. Meloon}, journal = {SIAM J. Sci. Comp.}, title = {Computing periodic orbits and their bifurcations with automatic differentiation}, year = {2000}, pages = {951--985}, volume = {22}, doi = {10.1137/S1064827599359278}, } @Article{GMK04, Title = {Topological characterization of spatial-temporal chaos}, Author = {M. Gameiro and W. Kalies and K. Mischaikow}, Journal = {Phys. Rev. E}, Year = {2004}, Pages = {035203}, Volume = {70}, DOI = {10.1103/PhysRevE.70.035203} } @Article{GNZ85, Title = {Accelerated diffusion in {Josephson} junctions and related chaotic systems}, Author = {T. Geisel and J. Nierwetberg and A. Zacherl}, Journal = {Phys. Rev. Lett.}, Year = {1985}, Pages = {616}, Volume = {54}, DOI = {10.1103/PhysRevLett.54.616} } @Book{goldstein01, author = {Goldstein, H. and Poole, C. P. and Safko, J. L.}, publisher = {Wesley}, title = {{Classical Mechanics}}, year = {2001}, address = {Reading, MA}, edition = {3}, } @Book{goldstein59, title = {{Classical Mechanics}}, publisher = {Wesley}, year = {1959}, author = {Goldstein, H.}, address = {Reading, MA}, } @Book{goldstein80, title = {{Classical Mechanics}}, publisher = {Wesley}, year = {1980}, author = {Goldstein, H.}, isbn = {9788177582833}, address = {Reading, MA}, edition = {2}, } @Inproceedings{Golse06, author = {Golse, F.}, title = {The periodic {Lorentz} gas in the {Boltzmann-Grad} limit}, booktitle = {{Proc. ICM - Madrid}}, year = {2006}, volume = {3}, pages = {183--203}, doi = {10.4171/022-3/9}, journal = {Proc. ICM (Madrid, 2006)}, } @Article{Golse08, Title = {On the periodic {Lorentz} gas and the {Lorentz} kinetic equation}, Author = {Golse, F.}, Journal = {Ann. Fac. Sci. Toulouse Math. S{\'e}r. 6}, Year = {2008}, Pages = {735--749}, Volume = {17}, DOI = {10.5802/afst.1200} } @InCollection{Golse12, author = {F. Golse}, booktitle = {{Nonlinear Partial Differential Equations}}, publisher = {Springer}, title = {Recent results on the periodic {Lorentz} gas}, year = {2012}, isbn = {978-3-0348-0190-4}, pages = {39--99}, doi = {10.1007/978-3-0348-0191-1_2}, } @Book{golubI, Title = {{Singularities and Groups in Bifurcation Theory}}, Author = {M. Golubitsky and D. G. Schaeffer}, Publisher = {Springer}, Year = {1984}, Address = {New York}, DOI = {10.1007/978-1-4612-5034-0}, ISBN = {9781461250340}, Volume = {1} } @Book{golubII, Title = {{Singularities and Groups in Bifurcation Theory}}, Author = {M. Golubitsky and I. Stewart and D. G. Schaeffer}, Publisher = {Springer}, Year = {1988}, Address = {New York}, DOI = {10.1007/978-1-4612-4574-2}, ISBN = {978-0-387-96652-6}, Volume = {2} } @Book{golubitsky2002sp, title = {{The Symmetry Perspective}}, publisher = {Birkh{\"a}user}, year = {2002}, author = {Golubitsky, M. and Stewart, I.}, isbn = {9783034881678}, address = {Boston}, doi = {10.1007/978-3-0348-8167-8}, } @Article{golubord, Title = {Order and disorder in fluid motion}, Author = {J. P. Gollub}, Journal = {Proc. Natl. Acad. Sci. USA}, Year = {1995}, Pages = {6705--6711}, Volume = {92}, DOI = {10.1073/pnas.92.15.6705} } @Article{golubsym84, author = {Golubitsky, M. and Swift, J. W. and Knobloch, J.}, journal = {Physica D}, title = {Symmetries and pattern selection in {Rayleigh-Bernard} convection}, year = {1984}, pages = {249}, volume = {10}, doi = {10.1016/0167-2789(84)90179-9}, } @Article{Gomez02, author = {A. G{\'o}mez and J. D. Meiss}, title = {Reversible polynomial automorphisms of the plane: {The} involutory case}, journal = {Phys. Lett. A}, year = {2003}, volume = {312}, pages = {49--58}, doi = {10.1016/S0375-9601(03)00605-4}, } @Article{Gomez04, Title = {Reversors and symmetries for polynomial automorphisms of the complex plane}, Author = {A. G\'omez and J. D. Meiss}, Journal = {Nonlinearity}, Year = {2004}, Pages = {975--1000}, Volume = {17}, DOI = {10.1088/0951-7715/17/3/012} } @Article{GoSuOr87, Title = {Stability and {Lyapunov} stability of dynamical systems: {A} differential approach and a numerical method}, Author = {Goldhirsch, I. and Sulem, P. L. and Orszag, S. A.}, Journal = {Physica D}, Year = {1987}, Pages = {311--337}, Volume = {27}, DOI = {10.1016/0167-2789(87)90034-0} } @Article{Gouy1899, Author = {Gouy}, Year = {1899} } @Book{Govaerts00, title = {{Numerical Methods for Bifurcations of Dynamical Equilibria}}, publisher = {SIAM}, year = {2000}, author = {W. J. F. Govaerts}, isbn = {9780898714425}, address = {Philadelphia}, doi = {10.1137/1.9780898719543}, } @Book{GoVanLo96, author = {Golub, G. H. and Van Loan, C. F.}, publisher = {J. Hopkins Univ. Press}, title = {{Matrix Computations}}, year = {2013}, address = {Baltimore, MD}, edition = {4}, isbn = {1421407949}, } @Article{GoWen00, author = {Golse, F. and Wennberg, B.}, journal = {ESAIM: Math. Modelling Numer. Anal.}, title = {On the distribution of free path lengths for the periodic {Lorentz} gas {II}}, year = {2000}, pages = {1151--1163}, volume = {34}, doi = {10.1051/m2an:2000121}, } @Article{GOY88, Title = {Unstable periodic orbits and the dimensions of multifractal chaotic attractors}, Author = {C. Grebogi and E. Ott and J. A. Yorke}, Journal = {Phys. Rev. A}, Year = {1988}, Pages = {1711--1724}, Volume = {37}, DOI = {10.1103/PhysRevA.37.1711} } @Article{GozReu89, Title = {Algebraic characterization of ergodicity}, Author = {Gozzi, E and Reuter, M}, Journal = {Phys. Lett. B}, Year = {1989}, Pages = {383--392}, Volume = {233}, DOI = {10.1016/0370-2693(89)91327-0} } @Article{GozReu90b, Title = {Classical mechanics as a topological field theory}, Author = {Gozzi, E. and Reuter, M.}, Journal = {Phys. Lett. B}, Year = {1990}, Pages = {137--144}, Volume = {240}, DOI = {10.1016/0370-2693(90)90422-3} } @Article{GozReu94, Title = {{Lyapunov} exponents, path-integrals and forms}, Author = {Gozzi, E. and Reuter, M.}, Journal = {Chaos Solit. Fract.}, Year = {1994}, Pages = {1117--1139}, Volume = {4}, DOI = {10.1016/0960-0779(94)90026-4} } @Article{Gozzi88, Title = {Hidden {BRS} invariance in classical mechanics}, Author = {Gozzi, E.}, Journal = {Phys. Lett. B}, Year = {1988}, Pages = {525--528}, Volume = {201}, DOI = {10.1016/0370-2693(88)90611-9} } @Article{Gozzi94, Title = {Counting periodic trajectories via topological classical mechanics}, Author = {Gozzi, E.}, Journal = {Chaos Solit. Fract.}, Year = {1994}, Pages = {653--660}, Volume = {4}, DOI = {10.1016/0960-0779(94)90073-6} } @Article{GPRBF11, author = {Garcia, S. P. and Pinho, A. J. and Rodrigues, J. M. O. S. and Bastos, C. A. C. and Ferreira, P. J. S. G.}, title = {Minimal absent words in prokaryotic and eukaryotic genomes}, journal = {PLoS One}, year = {2011}, volume = {6}, pages = {e16065}, doi = {10.1371/journal.pone.0016065}, } @Article{grant67, author = {F. C. Grant and M. R. Feix}, title = {{Fourier-{Hermit}e} solutions of the {Vlasov} equations in the linearized limit}, journal = {Phys. Fluids}, year = {1967}, volume = {10}, pages = {696--702}, doi = {10.1063/1.1762177}, } @Article{GraPro83, Title = {Estimation of the {Kolmogorov} entropy from a chaotic signal}, Author = {Grassberger, P. and Procaccia, I.}, Journal = {Phys. Rev. A}, Year = {1983}, Pages = {2591--2593}, Volume = {28}, DOI = {10.1103/PhysRevA.28.2591} } @Article{GraPro83a, Title = {Characterization of strange attractors}, Author = {Grassberger, P. and Procaccia, I.}, Journal = {Phys. Rev. Lett.}, Year = {1983}, Pages = {346--349}, Volume = {50}, DOI = {10.1103/PhysRevLett.50.346} } @Article{GraPro83b, Title = {Measuring the strangeness of strange attractors}, Author = {Grassberger, P. and Procaccia, I.}, Journal = {Physica D}, Year = {1983}, Pages = {189--208}, Volume = {9}, DOI = {10.1016/0167-2789(83)90298-1} } @Book{GraRyz, author = {I. S. Gradshteyn and I. M. Ryzhik}, publisher = {Elsevier LTD, Oxford}, title = {{Tables of Integrals, Series and Products}}, year = {2014}, address = {New York}, edition = {8}, isbn = {0123849330}, } @Article{gras86, Title = {Toward a quantitative theory of self-generated complexity}, Author = {Grassberger, P.}, Journal = {Int. J. Theor. Phys.}, Year = {1986}, Pages = {907--938}, Volume = {25}, DOI = {10.1007/BF00668821}, } @Article{grass88, author = {Grassberger, P.}, journal = {Z. Naturf. A}, title = {On symbolic dynamics of one-humped maps of the interval}, year = {1988}, pages = {671--680}, volume = {43}, doi = {10.1515/zna-1988-0710}, } @Article{grass89, Title = {On the symbolic dynamics of {H{\'e}non} map}, Author = {P. Grassberger and H. Kantz and U. Moenig}, Journal = {J. Phys. A}, Year = {1989}, Pages = {5217--5230}, Volume = {22}, DOI = {10.1088/0305-4470/22/24/011} } @Article{Grassberger89, author = {P. Grassberger}, title = {Information content and predictability of lumped and distributed dynamical systems}, journal = {Phys. Scr.}, year = {1989}, volume = {40}, pages = {346}, doi = {10.1088/0031-8949/40/3/016}, } @Article{GrBaPo88, Title = {Scaling laws for invariant measures on hyperbolic and nonhyperbolic atractors}, Author = {Grassberger, P. and Badii, R. and Politi, A.}, Journal = {J. Stat. Phys.}, Year = {1988}, Pages = {135--178}, Volume = {51}, DOI = {10.1007/BF01015324}, } @Article{greb1, Title = {Unstable periodic orbits and the dimension of chaotic attractors}, Author = {C. Grebogi and E. Ott and J. A. Yorke}, Journal = {Phys. Rev. A}, Year = {1987}, Pages = {3522--3524}, Volume = {36}, DOI = {10.1103/PhysRevA.36.3522} } @Article{greb90shad, Title = {Shadowing of physical trajectories in chaotic dynamics: {Containment} and refinement}, Author = {C. Grebogi and S. M. Hammel and J. A. Yorke and T. Sauer}, Journal = {Phys. Rev. Lett.}, Year = {1990}, Pages = {1527--1530}, Volume = {65}, DOI = {10.1103/PhysRevLett.65.1527} } @Incollection{GrebogiOttYorke04, author = {C. Grebogi and E. Ott and J. A. Yorke}, title = {Unstable periodic orbits and the dimensions of multifractal chaotic attractors}, booktitle = {{The Theory of Chaotic Attractors}}, publisher = {Springer}, year = {2004}, editor = {Hunt, B. R. and Li, T.-Y. and Kennedy, J. A. and Nusse, H. E.}, isbn = {978-1-4419-2330-1}, pages = {335--348}, address = {New York}, doi = {10.1007/978-0-387-21830-4_19}, } @Article{GrebogiYorke:83, Title = {Crises, sudden changes in chaotic attractors, and transient chaos}, Author = {C. Grebogi and E. Ott and J. A. Yorke}, Journal = {Physica D}, Year = {1983}, Pages = {181--200}, Volume = {7}, DOI = {10.1016/0167-2789(83)90126-4} } @Book{Grece06, title = {{New Developments in String Theory Research}}, publisher = {Nova Science Publishers}, year = {2006}, author = {Grece, S. A.}, isbn = {9781594544880}, } @Article{gree79, Title = {A method for determining a stochastic transition}, Author = {J. M. Greene}, Journal = {J. Math. Phys.}, Year = {1979}, Pages = {1183--1201}, Volume = {20}, DOI = {10.1063/1.524170} } @Article{gree98, Title = {Two-dimensional measure-preserving mappings}, Author = {J. M. Greene}, Journal = {J. Math. Phys.}, Year = {1968}, Pages = {760}, Volume = {9}, DOI = {10.1063/1.1664639} } @Article{GreeKim87, Title = {The calculation of {Lyapunov} spectra}, Author = {J. M. Greene and J.-S. Kim}, Journal = {Physica D}, Year = {1987}, Pages = {213--225}, Volume = {24}, DOI = {10.1016/0167-2789(87)90076-5} } @Article{Grem05, Title = {Semiclassical analysis of real atomic spectra beyond {Gutzwiller}'s approximation}, Author = {Gr{\'e}maud, B.}, Journal = {Phys. Rev. E}, Year = {2005}, Pages = {046208}, Volume = {72}, DOI = {10.1103/PhysRevE.72.046208} } @Book{greshosani, title = {{Incompressible Flow and the Finite Element Method}}, publisher = {Wiley}, year = {2000}, author = {P. M. Gresho and R. L. Sani}, address = {New York}, } @Article{GrMaViFe81, Title = {Universal behaviour in families of area-preserving maps}, Author = {J. M. Greene and R. S. MacKay and F. Vivaldi and M. J. Feigenbaum}, Journal = {Physica D}, Year = {1981}, Pages = {468--486}, Volume = {3}, DOI = {10.1016/0167-2789(81)90034-8} } @Article{Gro, Title = {La th{\'e}orie de {Fredholm}}, Author = {A. Grothendieck}, Journal = {Bull. Soc. Math. France}, Year = {1956}, Pages = {319--384}, Volume = {84}, URL = {http://eudml.org/doc/86908} } @Article{GrOcCo11, Title = {Targeting ballistic lunar capture trajectories using periodic orbits}, Author = {Griesemer, P. R. and Ocampo, C. and Cooley, D. S.}, Journal = {J. Guidance, Control and Dynamics}, Year = {2011}, Pages = {893--902}, Volume = {34}, DOI = {10.2514/1.46843} } @Article{GroFuj82, Title = {Diffusion in discrete nonlinear dynamical systems}, Author = {Grossmann, S. and Fujisaka, H.}, Journal = {Phys. Rev. A}, Year = {1982}, Pages = {1779--1782}, Volume = {26}, DOI = {10.1103/PhysRevA.26.1779} } @Article{GroFuj82b, Title = {Chaos-induced diffusion in nonlinear discrete dynamics}, Author = {Fujisaka, H. and Grossmann, S.}, Journal = {Z. Phys. B}, Year = {1982}, Pages = {261--275}, Volume = {48}, DOI = {10.1007/BF01420589} } @Article{GroTho77, Title = {Invariant distributions and stationary correlation functions of one-dimensional discrete processes}, Author = {S. Grossmann and S. Thomae}, Journal = {Z. Naturf. A}, Year = {1977}, Pages = {1353--1363}, Volume = {32}, DOI = {10.1515/zna-1977-1204} } @Article{GroTho83, author = {Grossmann, S. and Thomae, S.}, title = {Shape dependence of correlation times in chaos-induced diffusion}, journal = {Phys. Lett. A}, year = {1983}, volume = {97}, pages = {263--267}, doi = {10.1016/0375-9601(83)90685-0}, } @Article{GRT89, Title = {Hidden {BRS} invariance in classical mechanics. {II}}, Author = {Gozzi, E. and Reuter, M. and Thacker, W. D.}, Journal = {Phys. Rev. D}, Year = {1989}, Pages = {3363--3377}, Volume = {40}, DOI = {10.1103/PhysRevD.40.3363} } @Article{GRT92a, Title = {Symmetries of the classical path integral on a generalized phase-space manifold}, Author = {Gozzi, E. and Reuter, M. and Thacker, W. D.}, Journal = {Phys. Rev. D}, Year = {1992}, Pages = {757--765}, Volume = {46}, DOI = {10.1103/PhysRevD.46.757} } @Article{GRT92b, Title = {On the {Toda} criterion}, Author = {Gozzi, E. and Reuter, M. and Thacker, W. D.}, Journal = {Chaos Solit. Fract.}, Year = {1992}, Pages = {441--458}, Volume = {2}, DOI = {10.1016/0960-0779(92)90019-J} } @Article{GSK83, author = {Gol'berg, A. I. and Sinai, Ya. G. and Khanin, K. M.}, journal = {Russ. Math. Surv.}, title = {Universal properties for sequences of bifurcations of period 3}, year = {1983}, pages = {187--188}, volume = {38}, doi = {10.1070/RM1983v038n01ABEH003398}, } @Article{Guck08, author = {J. Guckenheimer}, title = {{Piecewise-Smooth Dynamical Systems, by C. J. Budd, A. R. Champneys and P. Kowalczyk ({\em Book Review})}}, journal = {SIAM Rev.}, year = {2008}, volume = {50}, pages = {606--609}, url = {http://www.jstor.org/stable/20454156}, } @Book{guckb, title = {{Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields}}, publisher = {Springer}, year = {1983}, author = {J. Guckenheimer and P. Holmes}, address = {New York}, doi = {10.1007/978-1-4612-1140-2}, } @Article{Guckenh77, Title = {On the bifurcation of maps of the interval}, Author = {J. Guckenheimer}, Journal = {Inv. Math.}, Year = {1977}, Pages = {165--178}, Volume = {39}, DOI = {10.1007/BF01390107} } @Article{Guckenheimer70, author = {Guckenheimer, J.}, journal = {Bull. Amer. Math. Soc.}, title = {Axiom {A + NO }cycles {$\to \zeta_f(t)$} rational}, year = {1970}, pages = {592--594}, volume = {76}, doi = {10.1090/S0002-9904-1970-12449-1}, } @Article{Guckenheimer79b, author = {J. Guckenheimer and R. Williams}, journal = {Publ. Math. IHES}, title = {Structural stability of the {Lorenz} attractor}, year = {1979}, pages = {55--72}, volume = {50}, doi = {10.1007/BF02684769.pdf}, } @Book{GuiSte90, author = {V. Guillemin and S. Sternberg}, publisher = {Cambridge Univ. Press}, title = {{Symplectic Techniques in Physics}}, year = {1990}, address = {Cambridge UK}, isbn = {9780521389907}, } @Article{GuiUri87, Title = {Reduction, the trace formula, and semiclassical asymptotics}, Author = {Guillemin, V. and Uribe, A.}, Journal = {Proc. Natl. Acad. Sci. USA}, Year = {1987}, Pages = {7799--7801}, Volume = {84}, DOI = {10.1073/pnas.84.22.7799} } @Article{GuiUri90, Title = {Reduction and the trace formula}, Author = {Guillemin, V. and Uribe, A.}, Journal = {J. Diff. Geom.}, Year = {1990}, Pages = {315--347}, Volume = {32}, URL = {http://projecteuclid.org/euclid.jdg/1214445310} } @Misc{GuRiSf14, author = {{Gurau}, R. and {Rivasseau}, V. and {Sfondrini}, A.}, title = {Renormalization: {An} advanced overview}, year = {2014}, eprint = {1401.5003}, eprinttype = {arxiv}, } @Book{Gurtin81, title = {{An Introduction to Continuum Mechanics}}, publisher = {Academic}, year = {1981}, author = {Gurtin, M.E.}, isbn = {9780080918495}, address = {New York}, doi = {10.1115/1.3167763}, } @Book{Gusfield97, author = {Gusfield, D.}, publisher = {Cambridge Univ. Press}, title = {{Algorithms on Strings, Trees and Sequences: Computer Science and Computational Biology}}, year = {1997}, address = {Cambridge UK}, doi = {10.1017/CBO9780511574931}, } @Article{gut82, Title = {The quantization of a classically ergodic system}, Author = {M. C. Gutzwiller}, Journal = {Physica D}, Year = {1982}, Pages = {183--207}, Volume = {5}, DOI = {10.1016/0167-2789(82)90017-3} } @Book{gutbook, title = {{Chaos in Classical and Quantum Mechanics}}, publisher = {Springer}, year = {1990}, author = {M. C. Gutzwiller}, address = {New York}, doi = {10.1007/978-1-4612-0983-6}, } @Article{GutOsi15, author = {Gutkin, B. and Osipov, V.}, title = {Classical foundations of many-particle quantum chaos}, journal = {Nonlinearity}, year = {2016}, volume = {29}, pages = {325--356}, doi = {10.1088/0951-7715/29/2/325}, } @Article{gutzwiller67, Title = {Phase-integral approximation in momentum space and the bound states of an atom}, Author = {M. C. Gutzwiller}, Journal = {J. Math. Phys.}, Year = {1967}, Pages = {1979--2000}, Volume = {8}, DOI = {10.1063/1.1705112} } @Article{gutzwiller69, Title = {Phase-integral approximation in momentum space and the bound states of an atom. {II}}, Author = {M. C. Gutzwiller}, Journal = {J. Math. Phys.}, Year = {1969}, Pages = {1004--1020}, Volume = {10}, DOI = {10.1063/1.1664927} } @Article{gutzwiller70, Title = {Energy spectrum according to classical mechanics}, Author = {M. C. Gutzwiller}, Journal = {J. Math. Phys.}, Year = {1970}, Pages = {1791--1806}, Volume = {11}, DOI = {10.1063/1.1665328} } @Article{gutzwiller71, Title = {Periodic orbits and classical quantization conditions}, Author = {M. C. Gutzwiller}, Journal = {J. Math. Phys.}, Year = {1971}, Pages = {343--358}, Volume = {12}, DOI = {10.1063/1.1665596} } @Article{Gya, Title = {Atomic friction}, Author = {T. Gyalog and H. Thomas}, Journal = {Z. Phys. B}, Year = {1997}, Pages = {669--674}, Volume = {104}, DOI = {10.1007/s002570050506} } @Article{HakenZeroLyap83, Title = {At least one {Lyapunov} exponent vanishes if the trajectory of an attractor does not contain a fixed point}, Author = {H. Haken}, Journal = {Phys. Lett. A}, Year = {1983}, Pages = {71--72}, Volume = {94}, DOI = {10.1016/0375-9601(83)90209-8} } @Article{HaKiWa95, Title = {Regeneration mechanisms of near-wall turbulence structures}, Author = {J. Hamilton and J. Kim and F. Waleffe}, Journal = {J. Fluid Mech.}, Year = {1995}, Pages = {317--348}, Volume = {287}, DOI = {10.1017/S0022112095000978} } @PhdThesis{HalcrowThesis, author = {Halcrow, J.}, title = {{Geometry of Turbulence: An Exploration of the State-space of Plane {Couette} Flow}}, school = {School of Physics, Georgia Inst. of Technology}, year = {2008}, address = {Atlanta}, url = {http://ChaosBook.org/projects/theses.html}, } @Book{Hale63, Title = {{Oscillations in Nonlinear Systems}}, Author = {Hale, J. K.}, Publisher = {Dover}, Year = {1963}, Address = {New York}, ISBN = {9780486803265} } @Book{haleinf84, title = {{An Introduction to Infinite Dimensional Dynamical Systems - Geometric Theory}}, publisher = {Springer}, year = {1984}, author = {Rybakowski, K. P. and Hale, J. K. and Magalhaes, L. T. and Oliva, W. M.}, address = {New York}, isbn = {9781475744934}, doi = {10.1007/978-1-4757-4493-4}, } @Book{HaleKo91, title = {{Dynamics and Bifurcations}}, publisher = {Springer}, year = {1991}, author = {J. Hale and H. Ko{\c{c}}ak}, address = {New York}, doi = {10.1007/978-1-4612-4426-4}, } @Book{haleob, title = {{Ordinary Differential Equations}}, publisher = {Dover}, year = {1969}, author = {Hale, J. K.}, address = {New York}, isbn = {9780486472119}, } @Book{Hall03, author = {Hall, B. C.}, publisher = {Springer}, title = {{Lie Groups, {Lie} Algebras, and Representations}}, year = {2003}, address = {New York}, doi = {10.1007/978-1-4614-7116-5_16}, } @Book{halmos:fdvs, Title = {{Finite-Dimensional Vector Spaces}}, Author = {P. R. Halmos}, Publisher = {Princeton Univ. Press}, Year = {1948}, Address = {Princeton NJ}, ISBN = {9780691090955} } @Book{HaLuWa02, author = {Hairer, Ch. and Lubich and Wanner, G.}, publisher = {Springer}, title = {{Geometric Numerical Integration}}, year = {2002}, address = {New York}, isbn = {978-3-642-05157-9}, doi = {10.1007/978-3-662-05018-7}, } @Book{ham, Title = {{Hamiltonian Dynamical Systems: A Reprint Selection}}, Author = {MacKay, R. S. and Meiss, J. D.}, Publisher = {Taylor \& Francis}, Year = {1987}, Address = {Oxford}, ISBN = {9780852742167} } @Incollection{HamAnd07, author = {Hampikian, G. and Andersen, T. L.}, title = {Absent sequences: nullomers and primes}, booktitle = {{Pacific Symposium on Biocomputing}}, publisher = {World Scientific}, year = {2007}, editor = {Altman, R.}, isbn = {9789812772435}, pages = {355--366}, address = {Singapore}, doi = {10.1142/9789812772435_0034}, } @Article{HaMe98, Title = {Reduction of three-dimensional, volume-preserving flows with symmetry}, Author = {G. Haller and I. Mezi{\'c}}, Journal = {Nonlinearity}, Year = {1998}, Pages = {319--339}, Volume = {11}, DOI = {10.1088/0951-7715/11/2/008} } @Book{hamer, title = {{Group Theory and Its Application to Physical Problems}}, publisher = {Dover}, year = {1962}, author = {M. Hamermesh}, isbn = {9780486661810}, address = {New York}, doi = {10.1119/1.1941790}, } @Article{Hampikian2007, Title = {Absent sequences: Nullomers and primes}, Author = {Hampikian, G. and Andersen, T.}, Journal = {Pac. Symp. Biocomput.}, Year = {2007}, Pages = {355--366}, Volume = {12}, DOI = {10.1142/9789812772435_0034} } @Article{HanBer80, Title = {Quantization of linear maps on a torus -- {Fresnel} diffraction by a periodic grating}, Author = {J. H. Hannay and M. V. Berry}, Journal = {Physica D}, Year = {1980}, Pages = {267--290}, Volume = {1}, DOI = {10.1016/0167-2789(80)90026-3} } @PhdThesis{hansen_thesis, author = {Hansen, K. T.}, title = {{Symbolic Dynamics in Chaotic systems}}, school = {Univ. of Oslo}, year = {1993}, address = {Oslo, Norway}, url = {http://ChaosBook.org/projects/KTHansen/thesis}, } @Article{hansen1d, author = {Hansen, K. T. and Cvitanovi{\'c}, P.}, title = {Bifurcation structures in maps of {H{\'e}non} type}, journal = {Nonlinearity}, year = {1998}, volume = {11}, pages = {1233--1261}, doi = {10.1088/0951-7715/11/5/004}, } @Article{hansen92, author = {K. T. Hansen}, title = {Remarks on the symbolic dynamics for the {H{\'e}non} map}, journal = {Phys. Lett. A}, year = {1992}, volume = {165}, pages = {100--104}, doi = {10.1016/0375-9601(92)90083-X}, } @Article{Hansen92-1, author = {Hansen, K. T.}, title = {Symbolic dynamics. {I. Finite} dispersive billiards}, journal = {Nonlinearity}, year = {1993}, volume = {6}, pages = {753--769}, doi = {10.1088/0951-7715/6/5/005}, } @Article{Hansen92-2, author = {Hansen, K. T.}, title = {Symbolic dynamics. {II. Bifurcations} in billiards and smooth potentials}, journal = {Nonlinearity}, year = {1993}, volume = {6}, pages = {771--778}, doi = {10.1088/0951-7715/6/5/006}, } @Article{Hansen92b, author = {Hansen, K. T.}, title = {Pruning of orbits in four-disk and hyperbola billiards}, journal = {Chaos}, year = {1992}, volume = {2}, pages = {71--75}, doi = {10.1063/1.165900}, } @Article{Hansen95, author = {Hansen, K. T.}, title = {Alternative method to find orbits in chaotic systems}, journal = {Phys. Rev. E}, year = {1995}, volume = {52}, pages = {2388--2391}, doi = {10.1103/PhysRevE.52.2388}, } @Book{hao_symb, title = {{Elementary Symbolic Dynamics and Chaos in Dissipative Systems}}, publisher = {World Scientific}, year = {1989}, author = {Hao, B.-L.}, isbn = {978-9971-5-0698-8}, address = {Singapore}, doi = {10.1142/0674}, } @Book{hao90b, title = {{Chaos {II}}}, publisher = {World Scientific}, year = {1990}, author = {Hao, B.-L.}, address = {Singapore}, doi = {10.1142/1001}, } @Book{Hao98, title = {{Applied Symbolic Dynamics and Chaos}}, publisher = {World Scientific}, year = {2018}, author = {B.-L. Hao and W.-M. Zheng}, isbn = {9789813236448}, address = {Singapore}, edition = {2}, doi = {10.1142/10887}, } @Book{Harrison70, title = {{Solid State Theory}}, publisher = {Dover}, year = {1980}, author = {W. A. Harrison}, address = {New York}, } @Article{Harter69, Title = {Algebraic theory of ray representations of finite groups}, Author = {W. G. Harter}, Journal = {J. Math. Phys.}, Year = {1969}, Pages = {739--752}, Volume = {10}, DOI = {10.1063/1.1664901} } @Article{Harter78, author = {Harter, W. G. and dos Santos, N.}, title = {Double-group theory on the half-shell and the two-level system. {I. Rotation} and half-integral spin states}, journal = {Amer. J. Phys.}, year = {1978}, volume = {46}, pages = {251--263}, doi = {10.1119/1.11134}, } @Book{Harter93, Title = {{Principles of Symmetry, Dynamics, and Spectroscopy}}, Author = {Harter, W. G.}, Publisher = {Wiley}, Year = {1993}, Address = {New York}, URL = {http://www.uark.edu/ua/modphys/markup/PSDS_Info.html} } @Book{hartmanb, title = {{Ordinary Differential Equations}}, publisher = {Wiley}, year = {1964}, author = {P. Hartman}, address = {New York}, doi = {10.1137/1.9780898719222}, } @Article{HaSh92, author = {T. Harayama and A. Shudo}, journal = {J. Phys. A}, title = {Periodic orbits and semiclassical quantization of dispersing billiards}, year = {1992}, pages = {4595}, volume = {25}, doi = {10.1088/0305-4470/25/17/019}, } @Book{HasKat02, title = {{Handbook of Dynamical Systems}}, publisher = {Elsevier}, year = {2002}, author = {Hasselblatt, B. and Katok, A.}, volume = {1}, isbn = {9780080533445}, address = {New York}, } @Article{HasSaf, author = {H. H. Hasegawa and W. C. Saphir}, title = {Unitarity and irreversibility in chaotic systems}, journal = {Phys. Rev. A}, year = {1992}, volume = {46}, pages = {7401--7423}, doi = {10.1103/PhysRevA.46.7401}, } @Book{Hawk00, title = {{Emergence of the Theory of {Lie} Groups: {An} Assay in the History of Mathematics}}, publisher = {Springer}, year = {2000}, author = {Hawkins, T.}, isbn = {978-1-4612-7042-3}, address = {New York}, pages = {1869--1926}, } @Article{hbCreep, author = {H. Bruus and N. D. Whelan}, title = {Edge diffraction, trace formulae and the cardioid billiard}, journal = {Nonlinearity}, year = {1996}, volume = {9}, pages = {1023--1047}, doi = {10.1088/0951-7715/9/4/012}, } @Article{HBHL82, author = {D'Humieres, D. and Beasley, M. R. and Huberman, B. A. and Libchaber, A.}, title = {Chaotic states and routes to chaos in the forced pendulum}, journal = {Phys. Rev. A}, year = {1982}, volume = {26}, pages = {3483--3496}, doi = {10.1103/PhysRevA.26.3483} } @Article{HDB91, Title = {Calculations of periodic trajectories for the {H{\'e}non--Heiles Hamiltonian} using the monodromy method}, Author = {Davies, K. T. R. and Huston, T. E. and Baranger, M.}, Journal = {Chaos}, Year = {1992}, Pages = {215--224}, Volume = {2}, DOI = {10.1063/1.165907} } @Book{Hecht74, Title = {Optics}, Author = {Hecht, E.}, Publisher = {Addison-Wesley}, Year = {2016}, ISBN = {978-0133977226} } @Article{HeiStr10, Title = {Homotopies of eigenfunctions and the spectrum of the {Laplacian} on the {Sierpinski} carpet}, Author = {S. M. Heilman and R. S. Strichartz}, Journal = {Fractals}, Year = {2010}, Pages = {1--34}, Volume = {18}, DOI = {10.1142/S0218348X10004750}, URL = {http://www.math.ucla.edu/~heilman/papers/EigHomotopyV9Submit.pdf} } @Article{HeiZha07, Title = {Nonchaotic and chaotic behavior in three-dimensional quadratic systems: {Five}-one conservative cases}, Author = {J. Heidel and F. Zhang}, Journal = {Int. J. Bifur. Chaos}, Year = {2007}, Pages = {2049--2072}, Volume = {17}, DOI = {10.1142/S021812740701821X}, } @InProceedings{Hell77, Title = {Variational solutions of non-integrable systems}, Author = {R. H. G. Helleman}, Booktitle = {Topics in Nonlinear Dynamics, {AIP Conf. Proc. La Jolla} 1977}, Year = {1978}, Editor = {S. Jorna}, Pages = {264--85}, Volume = {46}, DOI = {10.1063/1.31422} } @Incollection{Hell79, author = {R. H. G. Helleman and T. Bountis}, title = {Periodic solutions of arbitrary period, variational methods}, booktitle = {{Stochastic Behavior in Classical and Quantum Hamiltonian Systems}}, publisher = {Springer}, year = {1979}, editor = {Casati, G. and Ford, J.}, isbn = {978-3-540-09120-2}, pages = {353--375}, address = {Berlin}, doi = {10.1007/BFb0021758}, } @Incollection{Hell80, Title = {Self-generated chaotic behavior in nonlinear mechanics}, Author = {Helleman, R. H. G.}, Booktitle = {{Fundamental Problems in Statistical Mechanics}}, Publisher = {North-Holland}, Year = {1980}, Address = {Amsterdam}, Editor = {E. G. D. Cohen}, ISBN = {9780444861375} } @Misc{Helleman, author = {Helleman, R. H. G.}, title = {{Fourier} series methods}, } @Article{HeMuAlBrHa07, author = {Heusler, S. and M\"uller, S. and Altland, A. and Braun, P. and Haake, F.}, title = {Periodic-orbit theory of level correlations}, journal = {Phys. Rev. Lett.}, year = {2007}, volume = {98}, pages = {044103}, doi = {10.1103/physrevlett.98.044103}, } @Article{HenLipCvi14, author = {J. M. Heninger and P. Cvitanovi{\'c} and D. Lippolis}, journal = {Phys. Rev. E}, title = {Neighborhoods of periodic orbits and the stationary distribution of a noisy chaotic system}, year = {2015}, pages = {062922}, volume = {92}, doi = {10.1103/PhysRevE.92.062922}, } @Article{henon, Title = {A two-dimensional mapping with a strange attractor}, Author = {M. H{\'e}non}, Journal = {Commun. Math. Phys.}, Year = {1976}, Pages = {69}, Volume = {50}, DOI = {10.1007/BF01608556} } @Article{Henon69, author = {M. H{\'e}non}, journal = {Quart. Appl. Math.}, title = {Numerical study of quadratic area-preserving mappings}, year = {1969}, pages = {291--312}, volume = {27}, doi = {10.1090/qam/253513}, } @Article{henon82, Title = {On the numerical computation of {Poincar{\'e}} maps}, Author = {M. H{\'e}non}, Journal = {Physica D}, Year = {1982}, Pages = {412--414}, Volume = {5}, DOI = {10.1016/0167-2789(82)90034-3} } @Book{henonrtb2, title = {{Generating Families in the {Restricted Three-Body} Problem {II. Quantitative} Study of Bifurcations}}, publisher = {Springer}, year = {2001}, author = {M. H{\'e}non}, address = {New York}, } @Article{HerGot10, author = {S. Hermann and G. A. Gottwald}, title = {The large core limit of spiral waves in excitable media: {A} numerical approach}, journal = {SIAM J. Appl. Dyn. Sys.}, year = {2010}, volume = {9}, pages = {536--567}, doi = {10.1137/090780055}, } @Article{Herold2008, Title = {Efficient computation of absent words in genomic sequences}, Author = {Herold, J. and Kurtz, S. and Giegerich, R.}, Journal = {BMC Bioinformatics}, Year = {2008}, Pages = {1--9}, Volume = {9}, DOI = {10.1186/1471-2105-9-167} } @Article{heron87, author = {J. M. Ghidaglia and B. H{\'e}ron}, title = {Dimension of the attractors associated to the {Ginzburg-Landau} partial differential equation}, journal = {Physica D}, year = {1987}, volume = {28}, pages = {282--304}, doi = {10.1016/0167-2789(87)90020-0}, } @Article{HesHol07, Title = {Crystallographic space groups in geometric algebra}, Author = {Hestenes, D. and Holt, J. W.}, Journal = {J. Math. Phys.}, Year = {2007}, Pages = {023514}, Volume = {48}, DOI = {10.1063/1.2426416}, URL = {http://geocalc.clas.asu.edu/pdf/CrystalGA.pdf} } @InCollection{Hestenes02, author = {Hestenes, D.}, booktitle = {{Applications of Geometric Algebra in Computer Science and Engineering}}, publisher = {Birkh{\"a}user}, title = {Point groups and space groups in geometric algebra}, year = {2002}, address = {Boston, MA}, editor = {Dorst, L. and Doran, C. and Lasenby, J.}, isbn = {978-1-4612-0089-5}, pages = {3--34}, doi = {10.1007/978-1-4612-0089-5_1}, url = {http://geocalc.clas.asu.edu/pdf/crystalsymmetry.pdf}, } @Article{Hestenes03, Title = {Spacetime physics with geometric algebra}, Author = {Hestenes, D.}, Journal = {Amer. J. Phys.}, Year = {2003}, Pages = {691--714}, Volume = {71}, DOI = {10.1119/1.1571836}, URL = {http://geocalc.clas.asu.edu/pdf/SpacetimePhysics.pdf} } @Article{Hestenes15, author = {Hestenes, D.}, journal = {Advances in Applied Clifford Algebras}, title = {The genesis of {Geometric Algebra}---a personal retrospective}, year = {2016}, pages = {351--379}, volume = {27}, doi = {10.1007/s00006-016-0664-z}, } @Book{Hestenes66, Title = {{Space-time Algebra}}, Author = {Hestenes, D.}, Publisher = {Springer}, Year = {1966}, DOI = {10.1007/978-3-319-18413-5}, Edition = {2}, ISBN = {978-3-319-18413-5} } @Incollection{Hestenes86, Title = {Clifford algebra and the interpretation of quantum mechanics}, Author = {Hestenes, D.}, Booktitle = {{Clifford Algebras and their Applications in Mathematical Physics}}, Publisher = {Springer}, Year = {1986}, Address = {Berlin}, Editor = {J. S. R. Chisholm and A. K. Common}, Pages = {321--346}, DOI = {10.1007/978-94-009-4728-3_27}, ISBN = {978-94-009-4728-3}, URL = {http://www2.montgomerycollege.edu/departments/planet/planet/Numerical_Relativity/caiqm.pdf} } @Book{Hestenes99, title = {{New Foundations for Classical Mechanics}}, publisher = {Springer}, year = {2006}, author = {Hestenes, D.}, isbn = {9780306471223}, address = {New York}, edition = {2}, doi = {10.1007/978-94-009-4802-0}, } @Article{HG01, Title = {Diffusion of particles bouncing on a one-dimensional periodically corrugated floor}, Author = {Harayama, T. and Gaspard, P.}, Journal = {Phys. Rev. E}, Year = {2001}, Pages = {036215}, Volume = {64}, DOI = {10.1103/PhysRevE.64.036215} } @Article{HGC08, Title = {Equilibrium and traveling-wave solutions of plane {Couette} flow}, Author = {Gibson, J. F. and Halcrow, J. and Cvitanovi{\'c}, P.}, Journal = {J. Fluid Mech.}, Year = {2009}, Pages = {243--266}, Volume = {638}, DOI = {10.1017/S0022112009990863} } @Article{HHKR50yChaos, author = {T. Hikihara and P. Holmes and T. Kambe and G. Rega}, title = {Fifty years of chaos: {Applied} and theoretical}, journal = {Chaos}, year = {2012}, volume = {22}, pages = {047501}, doi = {10.1063/1.4769035}, } @Article{hhrugh92, Title = {The correlation spectrum for hyperbolic analytic maps}, Author = {H. H. Rugh}, Journal = {Nonlinearity}, Year = {1992}, Pages = {1237}, Volume = {5}, DOI = {10.1088/0951-7715/5/6/003} } @Article{hhrugh94, Title = {On the asymptotic form and the reality of spectra of {Perron-Frobenius} operators}, Author = {H. H. Rugh}, Journal = {Nonlinearity}, Year = {1994}, Pages = {1055}, Volume = {7}, DOI = {10.1088/0951-7715/7/3/015} } @InProceedings{hhrugh95, author = {H. H. Rugh}, booktitle = {{XIth Intern. Congr. Math.Phys., Paris 1994}}, title = {Fredholm determinants for real-analytic hyperbolic diffeomorphisms of surfaces}, year = {1995}, address = {Cambridge UK}, editor = {Iagolnitzer, D.}, pages = {297--303}, publisher = {Cambridge Univ. Press}, isbn = {9781571460301}, } @Article{hhrugh96a, Title = {Generalized {Fredholm} determinants and {Selberg} zeta functions for {Axiom A} dynamical systems}, Author = {H. H. Rugh}, Journal = {Ergod. Theor. Dynam. Syst.}, Year = {1996}, Pages = {805--819}, Volume = {16}, DOI = {10.1017/S0143385700009111} } @Article{hhsys, Title = {The applicability of the third integral of motion: {Some} numerical experiments}, Author = {M. H{\'e}non and C. Heiles}, Journal = {Astron. J.}, Year = {1964}, Pages = {73--79}, Volume = {69}, DOI = {10.1086/109234} } @Article{Hilbert93, Title = {{{\"U}}ber die vollen {Invariantensysteme}}, Author = {Hilbert, D.}, Journal = {Math. Ann.}, Year = {1893}, Pages = {313--373}, Volume = {42}, DOI = {10.1007/BF01444162} } @Book{hille, title = {{Ordinary Differential Equations in the Complex Domain}}, publisher = {Dover}, year = {1997}, author = {E. Hille}, address = {New York}, doi = {10.1090/simon/002.2/03}, } @Book{Hille2, title = {{Analytic Function Theory}}, publisher = {AMS Chelsea Publishing}, year = {2005}, author = {Hille, E.}, volume = {2}, isbn = {9780821829141}, } @Book{hirsch:smale, title = {{Differential Equations, Dynamical Systems, and Linear Algebra}}, publisher = {Academic}, year = {1974}, author = {Hirsch, M. W. and Smale, S.}, isbn = {9780080873763}, address = {San Diego}, } @Article{Hirsch84, Title = {The dynamical systems approach to differential equations}, Author = {M. W. Hirsch}, Journal = {Bull. Amer. Math. Soc.}, Year = {1984}, Pages = {1--64}, Volume = {11}, DOI = {10.1090/S0273-0979-1984-15236-4} } @Article{hislop89, author = {P. D. Hislop and J. D. Crawford}, title = {Application of spectral deformation to the {Vlasov--Poisson} system. {II. Mathematical} results}, journal = {J. Math. Phys.}, year = {1989}, volume = {30}, pages = {2819--2837}, doi = {10.1063/1.528465}, } @Book{HiSmDe12, title = {{Differential Equations, Dynamical Systems, and an Introduction to Chaos}}, publisher = {Elsevier Science}, year = {2012}, author = {Hirsch, M. W. and Smale, S. and Devaney, R. L.}, isbn = {978-0-12-382010-5}, edition = {3}, } @Article{HitZe85, author = {Hitzl, D. L. and Zele, F.}, journal = {Physica D}, title = {An exploration of the {H}{\'e}non quadratic map}, year = {1985}, pages = {305--326}, volume = {14}, doi = {10.1016/0167-2789(85)90092-2}, } @Article{HJM03, author = {B. Hof and A. Juel and T. Mullin}, title = {Scaling of the turbulence transition threshold in a pipe}, journal = {Phys. Rev. Lett.}, year = {2003}, volume = {91}, pages = {244502}, doi = {10.1103/physrevlett.91.244502}, } @Book{HK03, author = {Hasselblatt, B. and Katok, A.}, publisher = {Cambridge Univ. Press}, title = {{A First Course in Dynamics: with a Panorama of Recent Developments}}, year = {2003}, address = {Cambridge UK}, doi = {10.1017/cbo9780511998188}, } @Article{HK82, author = {Hofbauer, F. and Keller, G.}, title = {Ergodic properties of invariant measures for piecewise monotonic transformations}, journal = {Math. Z.}, year = {1982}, volume = {180}, pages = {119--140}, doi = {10.1007/BF01215004} } @Article{HK84, author = {F. Hofbauer and G. Keller}, title = {Zeta-functions and transfer-operators for piecewise linear transformations}, journal = {J. Reine Angew. Math.}, year = {1984}, volume = {352}, pages = {100--113}, doi = {10.1515/crll.1984.352.100} } @Article{HKG02, Title = {Deterministic diffusion in flower-shaped billiards}, Author = {Harayama, Takahisa and Klages, Rainer and Gaspard, Pierre}, Journal = {Phys. Rev. E}, Year = {2002}, Pages = {026211}, Volume = {66}, DOI = {10.1103/PhysRevE.66.026211} } @Article{HKZhang11, Title = {Current in periodic {Lorentz} gases with twists}, Author = {Zhang, H.-K.}, Journal = {Commun. Math. Phys.}, Year = {2011}, Pages = {747--776}, Volume = {306}, DOI = {10.1007/s00220-011-1262-5} } @Article{HMR98, author = {Holm, D. D. and Marsden, J. E. and Ratiu, T. S.}, journal = {Adv. Math.}, title = {The {Euler-Poincar{\'e}} equations and semidirect products with applications to continuum theories}, year = {1998}, pages = {1--81}, volume = {137}, doi = {10.1006/aima.1998.1721}, } @Article{HNks86, Title = {The {Kuramoto-Sivashinsky} equation: a bridge between {PDE}'s and dynamical systems}, Author = {J. M. Hyman and B. Nicolaenko}, Journal = {Physica D}, Year = {1986}, Pages = {113--126}, Volume = {18}, DOI = {10.1016/0167-2789(86)90166-1} } @Article{HNZks86, author = {J. M. Hyman and B. Nicolaenko and S. Zaleski}, title = {Order and complexity in the {Kuramoto-Sivashinsky} model of weakly turbulent interfaces}, journal = {Physica D}, year = {1986}, volume = {23}, pages = {265--292}, doi = {10.1016/0167-2789(86)90136-3}, } @Article{Hofbauer85, author = {F. Hofbauer}, title = {Periodic points for piecewise monotonic transformations}, journal = {Ergod. Theor. Dynam. Syst.}, year = {1985}, volume = {5}, pages = {237--256}, doi = {10.1017/S014338570000287X}, } @Article{Hofbauer86, author = {Hofbauer, F.}, title = {Piecewise invertible dynamical systems}, journal = {Probab. Th. Rel. Fields}, year = {1986}, volume = {72}, pages = {359--386}, doi = {10.1007/BF00334191}, } @Book{hoffman:kunze, title = {{Linear Algebra}}, publisher = {Prentice-Hall}, year = {1971}, author = {K. Hoffman and R. Kunze}, address = {Englewood Cliffs NJ}, edition = {2}, doi = {10.2307/3617032}, } @Book{HoJo90, author = {Horn, R. A. and Johnson, C. R.}, publisher = {Cambridge Univ. Press}, title = {{Matrix Analysis}}, year = {2012}, address = {Cambridge UK}, doi = {10.1017/cbo9781139020411}, } @Book{Holden86, editor = {Holden, A. V.}, publisher = {Princeton Univ. Press}, title = {{Chaos}}, year = {1986}, address = {Princeton NJ}, isbn = {9781400858156}, doi = {10.1515/9781400858156}, } @Article{Holmes, Title = {The dynamics of repeated impacts with a sinusoidally vibrating table}, Author = {J. Guckenheimer and P. J. Holmes}, Journal = {J. Sound Vib.}, Year = {1982}, Pages = {173--189}, Volume = {84}, DOI = {10.1016/S0022-460X(82)80002-3} } @Article{Holmes05, author = {P. Holmes}, title = {Ninety plus thirty years of nonlinear dynamics: {Less} is more and more is different}, journal = {Int. J. Bifur. Chaos}, year = {2005}, volume = {15}, pages = {2703--2716}, doi = {10.1142/S0218127405013678}, } @Book{Holmes96, author = {P. Holmes and J. L. Lumley and G. Berkooz}, publisher = {Cambridge Univ. Press}, title = {{Turbulence, Coherent Structures, Dynamical Systems and Symmetry}}, year = {1996}, address = {Cambridge UK}, doi = {10.1017/cbo9780511622700}, } @Article{homcont, author = {Champneys, A. R. and Kuznetsov, Y. A. and Sandstede, B.}, title = {A numerical toolbox for homoclinic bifurcation analysis}, journal = {Int. J. Bifur. Chaos}, year = {1996}, volume = {6}, pages = {867--887}, doi = {10.1142/s0218127496000485}, } @Book{HoMoUl06, title = {{Introduction to Automata Theory, Languages, and Computation}}, publisher = {Addison-Wesley}, year = {2013}, author = {Hopcroft, J. E. and Motwani, R. and Ullman, J. D.}, isbn = {1292039051}, address = {Reading MA}, } @Article{HooHoo12, Title = {Local {Gram--Schmid}t and covariant {Lyapunov} vectors and exponents for three harmonic oscillator problems}, Author = {W. G. Hoover and C. G. Hoover}, Journal = {Commun. Nonlinear Sci. Numer. Simul.}, Year = {2012}, Pages = {1043--1054}, Volume = {17}, DOI = {10.1016/j.cnsns.2011.06.025} } @Article{hoopks85, author = {A. P. Hooper and R. Grimshaw}, title = {Nonlinear instability at the interface between two viscous fluids}, journal = {Phys. Fluids}, year = {1985}, volume = {28}, pages = {37--45}, doi = {10.1063/1.865160}, } @Book{hop, title = {{Introduction to Automata Theory, Languages and Computation}}, publisher = {Addison-Wesley}, year = {1979}, author = {J. E. Hopcroft and J. D. Ullman}, isbn = {81-7808-347-7.}, address = {Reading MA}, } @Book{hopf, title = {{Ergodentheorie}}, publisher = {Springer}, year = {1937}, author = {Hopf, E.}, isbn = {9783642866302}, series = {Ergebnisse der Mathematik und Ihrer Grenzgebiete. 1. Folge}, address = {Berlin}, doi = {10.1007/978-3-642-86630-2}, } @Article{hopf42, author = {Hopf, E.}, title = {{Abzweigung einer periodischen L\"{o}sung von einer station\"{a}ren L\"{o}sung eines Differentialsystems}}, journal = {Ber. S{\"a}chs. Akad. Wiss. Leipzig, Math.-Phys. Kl.}, year = {1942}, volume = {94}, pages = {3--22}, } @InCollection{hopf42transl, author = {Hopf, E.}, title = {Bifurcation of a periodic solution from a stationary solution of a system of differential equations}, booktitle = {{The Hopf Bifurcation and Its Applications}}, publisher = {Springer}, year = {1942}, editor = {Marsden, J. E. and McCracken, M.}, pages = {163--193}, address = {New York}, note = {Transl. by L. N. Howard and N. Kopell}, isbn = {9781461263746}, } @Article{hopf48, Title = {A mathematical example displaying features of turbulence}, Author = {E. Hopf}, Journal = {Commun. Pure Appl. Math.}, Year = {1948}, Pages = {303--322}, Volume = {1}, DOI = {10.1002/cpa.3160010401} } @Article{hopf50, author = {E. Hopf}, title = {The partial differential equation $u_t + uu_x = u_{xx}$}, journal = {Commun. Pure Appl. Math.}, year = {1950}, volume = {3}, pages = {201--230}, doi = {10.1002/cpa.3160030302}, } @Article{hopf52, author = {E. Hopf}, title = {Statistical hydromechanics and functional calculus}, journal = {J. Rat. Mech. Anal.}, year = {1952}, volume = {1}, pages = {87--123}, doi = {10.1512/iumj.1952.1.51004}, } @Book{HopKan14, author = {Blum, A. and Hopcroft, J. and Kannan, R.}, publisher = {Cambridge Univ. Press}, title = {{Foundations of Data Science}}, year = {2020}, address = {Cambridge UK}, doi = {10.1017/9781108755528}, } @Book{hoyll06, author = {R. Hoyle}, publisher = {Cambridge Univ. Press}, title = {{Pattern Formation: An Introduction to Methods}}, year = {2006}, address = {Cambridge UK}, doi = {10.1017/cbo9780511616051}, } @Article{HS04, Title = {Grammatical complexity for two-dimensional maps}, Author = {R. Hagiwara and A. Shudo}, Journal = {J. Phys. A}, Year = {2004}, Pages = {10545}, Volume = {37}, DOI = {10.1088/0305-4470/37/44/006} } @Article{HS04a, Title = {An algorithm to prune the area-preserving {H{\'e}non} map}, Author = {R. Hagiwara and A. Shudo}, Journal = {J. Phys. A}, Year = {2004}, Pages = {10521}, Volume = {37}, DOI = {10.1088/0305-4470/37/44/005} } @Article{HSGsize98, author = {M. C. Strain and H. S. Greenside}, title = {Size-dependent transition to high-dimensional chaotic dynamics in a two-dimensional excitable media}, journal = {Phys. Rev. Lett.}, year = {1998}, volume = {80}, pages = {2306--2309}, doi = {10.1103/physrevlett.80.2306}, } @Article{Hsu76, author = {I.-D. Hsu}, title = {Existence of periodic solutions for the {Belousov-Zaikin-Zhabotinskii} reaction by a theorem of {Hopf}}, journal = {J. Diff. Eqn.}, year = {1976}, volume = {20}, pages = {399--403}, doi = {10.1016/0022-0396(76)90116-9}, } @Book{Htf1, title = {{Higher Transcendental Functions}}, publisher = {McGraw-Hill}, year = {1953}, author = {A. Erd{\'e}lyi and W. Magnus and F. Oberhettinger and F. G. Tricomi}, volume = {1}, series = {Bateman Manuscript Project}, url = {http://authors.library.caltech.edu/43491/1/Volume%201.pdf}, } @Article{Hu, author = {B. Hu and B. Lin}, title = {{Yang-Lee} zeros, {Julia} sets, and their singularity spectr}, journal = {Phys. Rev. A}, year = {1989}, volume = {39}, pages = {4789}, doi = {10.1103/physreva.39.4789}, } @Article{Hurt93, author = {N. E. Hurt}, title = {Zeta functions and periodic orbit theory: {A} review}, journal = {Results in Mathematics}, year = {1993}, volume = {23}, pages = {55--120}, doi = {10.1007/BF03323131} } @Article{Hutchinson81, Title = {Fractals and self-similarity}, Author = {J. Hutchinson}, Journal = {Indiana Univ. Math. J.}, Year = {1981}, Pages = {713--747}, Volume = {30}, DOI = {10.1512/iumj.1981.30.30055}, URL = {http://maths-people.anu.edu.au/~john/Assets/Research%20Papers/fractals_self-similarity.pdf} } @Book{Huyg1673, title = {{L'Horloge \`a Pendule}}, publisher = {Swets \& Zeitlinger}, year = {1673}, author = {C. Huygens}, address = {Amsterdam}, } @Article{HV93, Title = {A family of rational zeta functions for the quadratic map}, Author = {S. Hatjispiros and F. Vivaldi}, Journal = {Nonlinearity}, Year = {1995}, Pages = {)321--332}, Volume = {8}, DOI = {10.1088/0951-7715/8/3/002} } @Article{HvO94, Title = {Semiclassical theory of transport in antidot lattices}, Author = {G. Hackenbroich and F. von Oppen}, Journal = {Z. Phys. B}, Year = {1995}, Pages = {157}, Volume = {97}, DOI = {10.1007/BF01307466} } @Book{HW79, title = {{An Introduction to the Theory of Numbers}}, publisher = {Oxford Univ. Press}, year = {1979}, author = {G. H. Hardy and E. M. Wright}, isbn = {9780198531715}, address = {Oxford}, doi = {10.2307/3610026}, } @Article{HW90, Title = {Spectral properties of strongly perturbed {Coulomb} systems: {Fluctuation} properties}, Author = {H\"onig, A. and Wintgen, D.}, Journal = {Phys. Rev. A}, Year = {1989}, Pages = {5642--5657}, Volume = {39}, DOI = {10.1103/PhysRevA.39.5642} } @Article{HYG87, Title = {Do numerical orbits of chaotic dynamical processes represent true orbits?}, Author = {S. M. Hammel and J. A. Yorke and C. Grebogi}, Journal = {J. Complexity}, Year = {1987}, Pages = {136--145}, Volume = {3}, DOI = {10.1016/0885-064X(87)90024-0} } @Article{IMO96, author = {A. Ibort and C. Ontalba}, title = {Periodic orbits of {Hamiltonian} systems and symplectic reduction}, journal = {J. Phys. A}, year = {1996}, volume = {29}, pages = {675}, doi = {10.1088/0305-4470/29/3/018} } @Book{ince, title = {{Ordinary Differential Equations}}, publisher = {Dover}, year = {1956}, author = {E. L. Ince}, isbn = {9780486603490}, address = {New York}, doi = {10.2307/3605524}, } @Book{infdymnon, title = {{Infinite-Dimensional Dynamical Systems in Mechanics and Physics}}, publisher = {Springer}, year = {2013}, author = {T{\'e}mam, R.}, isbn = {9781461206453}, address = {New York}, edition = {2}, doi = {10.1007/978-1-4612-0645-3}, } @Article{inv, Title = {Invariant measurement of strange sets in terms of cycles}, Author = {P. Cvitanovi{\'c}}, Journal = {Phys. Rev. Lett.}, Year = {1988}, Pages = {2729--2732}, Volume = {61}, DOI = {10.1103/PhysRevLett.61.2729} } @Book{IooAde98, title = {{Topics in Bifurcation Theory and Applications}}, publisher = {World Scientific}, year = {1998}, author = {Iooss, G. and Adelmeyer, M.}, isbn = {9789810237288}, address = {Singapore}, doi = {10.1142/3990}, } @Article{Isaeva, author = {O. B. Isaeva and V. I. Ponomarenko and S. P. Kuznetsov}, title = {Mandelbrot set in coupled logistic maps and in an electronic experiment}, journal = {Phys. Rev. E.}, year = {2001}, volume = {6}, pages = {055201}, doi = {10.1103/physreve.64.055201}, } @Misc{Isaeva_h, author = {O. B. Isaeva and S. P. Kuznetsov}, title = {Period-tripling accumulation point for complexified {H{\'e}non} map}, year = {2005}, url = {https://arXiv.org/abs/nlin/0509015}, } @Article{Isaeva2, author = {O. B. Isaeva}, title = {Fourier spectrum of the signal generated at the point of period tripling bifurcation accumulation}, journal = {Tech. Phys.}, year = {2006}, volume = {51}, pages = {929--931}, doi = {10.1134/S106378420607019X}, url = {http://sgtnd.narod.ru/papers0/2006TPE.pdf}, } @Article{IsaKuz00, author = {O. B. Isaeva and S. P. Kuznetsov}, title = {On scaling properties of two-dimensional maps near the accumulation point of the period-tripling cascade}, journal = {Regul. Chaotic. Dyn.}, year = {2005}, volume = {5}, pages = {459--476}, url = {http://rcd.ics.org.ru/upload/iblock/484/RCD050406.pdf}, } @Misc{IsaKuz05, author = {O. B. Isaeva and S. P. Kuznetsov}, title = {On possibility of realization of the phenomena of complex analytic dynamics in physical systems. {Novel} mechanism of the synchronization loss in coupled period-doubling systems}, year = {2005}, url = {https://arXiv.org/abs/nlin/0509012}, } @Article{IsaKuz05c, Title = {Approximate description of the {Mandelbrot} set. {Thermodynamic} analogy}, Author = {O. B. Isaeva and S. P. Kuznetsov}, Journal = {Nonlin. Phen. Compl. Syst.}, Year = {2005}, Pages = {157--165}, Volume = {8}, URL = {http://sgtnd.narod.ru/papers0/2005NPCS.pdf} } @Book{isham99, title = {{Modern Differential Geometry for Physicists}}, publisher = {World Scientific}, year = {1999}, author = {C. J. Isham}, isbn = {978-981-02-3562-8}, address = {Singapore}, edition = {2}, doi = {10.1142/3867}, } @Article{Ishii97, author = {Ishii, Y.}, title = {Towards a kneading theory for {Lozi} mappings {I: A} solution of the pruning front conjecture and the first tangency problem}, journal = {Nonlinearity}, year = {1997}, volume = {10}, pages = {731--747}, doi = {10.1088/0951-7715/10/3/008}, } @Article{Ishii97a, author = {Ishii, Y.}, title = {Towards a kneading theory for {Lozi mappings}. {II}: {Monotonicity} of the topological entropy and {Hausdorff} dimension of attractors}, journal = {Commun. Math. Phys.}, year = {1997}, volume = {190}, pages = {375--394}, doi = {10.1007/s002200050245}, } @Article{Ishimura02, Title = {Remarks on third-order {ODEs} relevant to the {Kuramoto--Sivashinsky} equation}, Author = {N. Ishimura}, Journal = {J. Diff. Eqn.}, Year = {2002}, Pages = {466--477}, Volume = {178}, DOI = {10.1006/jdeq.2001.4018} } @Article{IshNak00, Title = {Nonexistence of monotonic solutions of some third-order ode relevant to the {Kuramoto-Sivashinsky} equation}, Author = {Ishimura, N. and Nakamura, M.}, Journal = {Taiwanese J. Math.}, Year = {2000}, Pages = {621--625}, Volume = {4}, URL = {http://journal.tms.org.tw/index.php/TJM/article/view/1296} } @Article{Iso02, Title = {On the spectrum of {Farey} and {Gauss} maps}, Author = {S. Isola}, Journal = {Nonlinearity}, Year = {2002}, Pages = {1521--1539}, Volume = {15}, DOI = {10.1088/0951-7715/15/5/310} } @Misc{Iso95, author = {S. Isola}, title = {Dynamical zeta functions for non--uniformly hyperbolic transformations}, year = {1995}, url = {http://www.uvm.edu/pdodds/files/papers/others/1995/isola1995a.pdf}, } @Article{Iso99, Title = {Renewal sequences and intermittency}, Author = {Isola, S.}, Journal = {J. Stat. Phys.}, Year = {1999}, Pages = {263--280}, Volume = {97}, DOI = {10.1023/A:1004623303471} } @Article{Isola90, Title = {{$\zeta$}-functions and distribution of periodic orbits of toral automorphisms}, Author = {S. Isola}, Journal = {Europhys. Lett.}, Year = {1990}, Pages = {517--522}, Volume = {11}, DOI = {10.1209/0295-5075/11/6/006} } @Article{IsoPol90, author = {Isola, S. and Politi, A.}, title = {Universal encoding for unimodal maps}, journal = {J. Stat. Phys.}, year = {1990}, volume = {61}, pages = {263--291}, doi = {10.1007/BF01013965} } @Article{IT01, author = {T. Itano and S. Toh}, title = {The dynamics of bursting process in wall turbulence}, journal = {J. Phys. Soc. Japan}, year = {2001}, volume = {70}, pages = {703--716}, doi = {10.1143/jpsj.70.703}, } @Book{ItzDrouf91I, author = {Itzykson, C. and Drouffe, J. M.}, publisher = {Cambridge Univ. Press}, title = {{Statistical Field Theory: From Brownian Motion to Renormalization and Lattice Gauge Theory}}, year = {1991}, address = {Cambridge UK}, isbn = {9780521408059}, volume = {1}, } @Book{ItzDrouf91II, author = {Itzykson, C. and Drouffe, J. M.}, publisher = {Cambridge Univ. Press}, title = {{Statistical Field Theory: Strong Coupling, Monte Carlo Methods, Conformal Field Theory and Random Systems}}, year = {1991}, address = {Cambridge UK}, isbn = {9780521408066}, volume = {2}, } @Article{IzhiEquil, author = {E. M. Izhikevich}, title = {Equilibrium}, journal = {Scholarpedia}, year = {2007}, volume = {2}, number = {10}, pages = {2014}, doi = {10.4249/scholarpedia.2014}, } @Article{Jac46, Title = {{{{\"U}}ber ein leichtes Verfahren die in der Theorie der S{\"a}cul{\"a}rst{\"o}rungen vorkommenden Gleichungen numerisch aufzul{\"o}sen}}, Author = {Jacobi, C. G. J.}, Journal = {J. Reine Angew. Math. ({Crelle})}, Year = {1846}, Pages = {51--94}, Volume = {30} } @Book{jackson89, author = {Jackson, E. A.}, publisher = {Cambridge Univ. Press}, title = {{Perspectives of Nonlinear Dynamics}}, year = {1989}, address = {Cambridge UK}, volume = {1}, doi = {10.1017/cbo9780511623974}, } @Book{jackson89-2, author = {Jackson, E. A.}, publisher = {Cambridge Univ. Press}, title = {{Perspectives of Nonlinear Dynamics}}, year = {1989}, address = {Cambridge UK}, volume = {2}, doi = {10.1017/cbo9780511623974}, } @Article{Jacobi1841, author = {Jacobi, C. G. J.}, title = {De functionibus alternantibus earumque divisione per productum e differentiis elementorum conflatum}, journal = {J. Reine Angew. Math. ({Crelle})}, year = {1841}, volume = {22}, pages = {439--452}, doi = {10.1515/crll.1841.22.360}, } @Book{Jacobi1969, title = {{Collected Works}}, publisher = {Amer. Math. Soc.}, year = {1969}, author = {Jacobi, C. G. J.}, address = {Providence R.I.}, } @Book{Jammer66, title = {{The Conceptual Development of Quantum Mechanics}}, publisher = {McGraw-Hill}, year = {1966}, author = {M. Jammer}, address = {New York}, isbn = {9780883186176}, } @Article{JBB83, Title = {Complete devil's staircase fractal dimension and universality of mode-locking structure in the circle map}, Author = {Jensen, M. H. and Bak, P. and Bohr, T.}, Journal = {Phys. Rev. Lett.}, Year = {1983}, Pages = {1637--1639}, Volume = {50}, DOI = {10.1103/PhysRevLett.50.1637} } @Article{JBB84, Title = {Transition to chaos by interaction of resonances in dissipative systems. {I. Circle maps}}, Author = {M. H. Jensen and P. Bak and T. Bohr}, Journal = {Phys. Rev. A}, Year = {1984}, Pages = {1960--1969}, Volume = {30}, DOI = {10.1103/PhysRevA.30.1960} } @Book{JBG97, title = {{Poincar{\'e} and the Three Body Problem}}, publisher = {Amer. Math. Soc.}, year = {1997}, author = {J. Barrow-Green}, address = {Providence R.I.}, isbn = {9780821803677}, } @Book{jeffb, author = {H. Jeffreys and B. Jeffreys}, publisher = {Cambridge Univ. Press}, title = {{Methods of Mathematical Physics}}, year = {2000}, address = {Cambridge UK}, edition = {3}, doi = {10.2307/3610518}, } @Article{Jefferies1920, Author = {Jefferies}, Year = {1920} } @Article{JePo02, Title = {Calculating {Hausdorff} dimension of {Julia} sets and {Kleinian} limit sets}, Author = {Jenkinson, O. and Pollicott, M.}, Journal = {Amer. J. Math.}, Year = {2002}, Pages = {495--545}, URL = {http://www.jstor.org/stable/25099125} } @Article{JGB86, author = {P. S. {Jang} and R. L. {Gran} and D. J. {Benney}}, title = {On the origin of streamwise vortices in a turbulent boundary layer}, journal = {J. Fluid Mech.}, year = {1986}, volume = {169}, pages = {109--123}, doi = {10.1017/s0022112086000551}, } @Article{Jiang, author = {Jiang, Y. and Morita, T. and Sullivan, D.}, journal = {Commun. Math. Phys.}, title = {Expanding direction of the period doubling operator}, year = {1992}, pages = {509--520}, volume = {144}, doi = {10.1007/BF02099180}, } @Article{JKSN05, author = {J. Jimenez and G. Kawahara and M. P. Simens and M. Nagata}, title = {Characterization of near-wall turbulence in terms of equilibrium and `bursting' solutions}, journal = {Phys. Fluids}, year = {2005}, volume = {17}, pages = {015105}, doi = {10.1063/1.1825451}, } @Article{JM91, Title = {The minimal flow unit in near-wall turbulence}, Author = {Jim{\'e}nez, J. and Moin, P.}, Journal = {J. Fluid Mech.}, Year = {1991}, Pages = {213--240}, Volume = {225}, DOI = {10.1017/S0022112091002033} } @Article{johnston04, author = {H. Johnston and J.-G. Liu}, journal = {J. Comp. Phys.}, title = {Accurate, stable and efficient {Navier-Stokes} solvers based on explicit treatment of the pressure term}, year = {2004}, pages = {221--259}, volume = {199}, doi = {10.1016/j.jcp.2004.02.009}, } @Article{jolly_evaluating_2000, author = {M. Jolly and R. Rosa and R. T{\'e}mam}, title = {Evaluating the dimension of an inertial manifold for the {Kuramoto-Sivashinsky} equation}, journal = {Adv. Diff. Equations}, year = {2000}, volume = {5}, pages = {31--66} } @Article{JoMueSi12, author = {C. H. Joyner and S. M\"uller and M. Sieber}, title = {Semiclassical approach to discrete symmetries in quantum chaos}, journal = {J. Phys. A}, year = {2012}, volume = {45}, pages = {205102}, doi = {10.1088/1751-8113/45/20/205102}, } @Book{jones_dynamics_1992, title = {{Dynamics Reported: Expositions in Dynamical Systems}}, publisher = {Springer}, year = {1992}, author = {Jones, C. K. R. T. and Kirchgraber, U. and Walther, H.-O. and Bielawski, R.}, address = {New York}, } @Article{JoPro87, Title = {Strong spatial resonance and travelling waves in {Benard} convection}, Author = {C. A. Jones and M. R. E. Proctor}, Journal = {Phys. Lett. A}, Year = {1987}, Pages = {224--228}, Volume = {121}, DOI = {10.1016/0375-9601(87)90008-9} } @Article{Jordan3, author = {C. R. Jordan and D. A. Jordan and J. H. Jordan}, title = {Reversible complex {H{\'e}non} maps}, journal = {Experiment. Math.}, year = {2002}, volume = {11}, pages = {339}, doi = {10.1080/10586458.2002.10504479} } @Misc{JordanJava, Title = {Iterations of the complex {H{\'e}non} map}, Author = {A. Jordan}, URL = {http://www.shef.ac.uk/~daj/henon/chm.html} } @Book{JoSa, author = {J. V. Jos{\'e} and E. J. Salatan}, publisher = {Cambridge Univ. Press}, title = {{Classical dynamics - A contemporary approach}}, year = {1998}, address = {Cambridge UK}, doi = {10.1017/cbo9780511803772}, } @Book{Joshi77, author = {Joshi, A. W.}, publisher = {New Age International}, title = {{Elements of Group Theory for Physicists}}, year = {1997}, address = {New Delhi, India}, isbn = {9788122409758}, } @Article{jrd, Title = {Chaotic scattering theory, thermodynamic formalism, and transport coefficients}, Author = {P. Gaspard and J. R. Dorfman}, Journal = {Phys. Rev. E}, Year = {1995}, Pages = {3525}, Volume = {52}, DOI = {10.1103/PhysRevE.52.3525} } @Article{JRT01, author = {M. Jolly and R. Rosa and R. T{\'e}mam}, title = {Accurate computations on inertial manifolds}, journal = {SIAM J. Sci. Comput.}, year = {2001}, volume = {22}, pages = {2216}, doi = {10.1137/s1064827599351738}, } @Article{JT63, author = {D. D. Joseph and L. N. Tao}, title = {Transverse velocity components in fully developed unsteady flows}, journal = {J. Appl. Mech.}, year = {1963}, volume = {30}, pages = {147--148}, doi = {10.1115/1.3630068}, } @Article{julia, Title = {M{\'e}moire sur l'it{\'e}ration des fonctions rationnelles}, Author = {G. Julia}, Journal = {J. Math. Pures et Appl.}, Year = {1918}, Pages = {47--246}, Volume = {1}, URL = {http://eudml.org/doc/234994} } @Article{Jung42, author = {H. W. E. Jung}, title = {{Uber ganze birationale Transformationen der Ebene}}, journal = {J. Reine Angew. Math.}, year = {1942}, volume = {184}, pages = {161--174}, url = {http://eudml.org/doc/150111}, } @Misc{Jung97, Title = {Some explicit formulas for the iteration of rational functions}, Author = {W. Jung}, Year = {1997}, URL = {http://mndynamics.com/papers/expl.pdf} } @Article{JuRi90, Title = {Classical chaotic scattering-periodic orbits, symmetries, multifractal invariant sets}, Author = {C. Jung and P. Richter}, Journal = {J. Phys. A}, Year = {1990}, Pages = {2847}, Volume = {23}, DOI = {10.1088/0305-4470/23/13/023} } @Article{JuScho87, Title = {Cantor set structures in the singularities of classical potential scattering}, Author = {C. Jung and H. J. Scholz}, Journal = {J. Phys. A}, Year = {1987}, Pages = {3607}, Volume = {20}, DOI = {10.1088/0305-4470/20/12/015} } @Article{K31, Title = {Hamiltonian systems and transformations in {Hilbert} space}, Author = {B. O. Koopman}, Journal = {Proc. Natl. Acad. Sci. USA}, Year = {1931}, Pages = {315}, Volume = {17}, DOI = {10.1073/pnas.17.5.315} } @Article{K84, author = {G. Keller}, title = {On the rate of convergence to equilibrium in one-dimensional systems}, journal = {Commun. Math. Phys.}, year = {1984}, volume = {96}, pages = {181--193}, doi = {10.1007/BF01240219} } @Article{Kac46, Title = {Random walk and the theory of {Brownian} motion}, Author = {Kac, M.}, Journal = {Amer. Math. Monthly}, Year = {1947}, Note = {Reprinted in ref. \cite{Wax}}, Pages = {369--391}, Volume = {54}, DOI = {10.2307/2304386} } @InProceedings{KaCoCa02, Title = {Are bred vectors the same as {Lyapunov} vectors?}, Author = {{Kalnay}, E. and {Corazza}, M. and {Cai}, M.}, Booktitle = {EGS XXVII General Assembly, Nice, 21-26 April 2002}, Year = {2002} } @Article{Kalman60, Title = {A new approach to linear filtering and prediction problems}, Author = {Kalman, R. E.}, Journal = {J. Basic Eng.}, Year = {1960}, Pages = {35--45}, Volume = {82}, DOI = {10.1115/1.3662552} } @Article{kantzg, Title = {Repellers, semi-attractors, and long-lived chaotic transients}, Author = {H. Kantz and P. Grassberger}, Journal = {Physica D}, Year = {1985}, Pages = {75--86}, Volume = {17}, DOI = {10.1016/0167-2789(85)90135-6} } @Article{KaSa05, author = {Kawasaki, M. and Sasa, S.}, title = {Statistics of unstable periodic orbits of a chaotic dynamical system with a large number of degrees of freedom}, journal = {Phys. Rev. E}, year = {2005}, volume = {72}, pages = {037202}, doi = {10.1103/physreve.72.037202}, } @Article{Kato03, author = {S. Kato and M. Yamada}, title = {Unstable periodic solutions embedded in a shell model turbulence}, journal = {Phys. Rev. E}, year = {2003}, volume = {68}, pages = {025302}, doi = {10.1103/physreve.68.025302}, } @Book{Kato80, title = {{Perturbation Theory for Linear Operators}}, publisher = {Springer}, year = {1980}, author = {Kato, T.}, address = {Berlin}, isbn = {9783662126783}, doi = {10.1007/978-3-662-12678-3}, note = {Chap. {X}, sects. 1.3--1.4}, } @Article{Katok80, Title = {{Lyapunov} exponents, entropy and periodic orbits for diffeomorphisms}, Author = {A. Katok}, Journal = {Publ. Math. IHES}, Year = {1980}, Pages = {137--173}, Volume = {51}, URL = {http://www.numdam.org/item?id=PMIHES_1980__51__137_0} } @Book{Katok95, author = {A. Katok and B. Hasselblatt}, publisher = {Cambridge Univ. Press}, title = {{Introduction to the Modern Theory of Dynamical Systems}}, year = {1995}, address = {Cambridge UK}, doi = {10.1017/cbo9780511809187}, } @Article{kavousanakis_projective_2007, author = {{M.E.} Kavousanakis and R. Erban and {A.G.} Boudouvis and {C.W.} Gear and {I.G.} Kevrekidis}, journal = {J. Comp. Phys.}, title = {Projective and coarse projective integration for problems with continuous symmetries}, year = {2007}, pages = {382--407}, volume = {225}, doi = {10.1016/j.jcp.2006.12.003}, } @Article{KawKida01, Title = {Periodic motion embedded in plane {Couette} turbulence: {Regeneration} cycle and burst}, Author = {G. Kawahara and S. Kida}, Journal = {J. Fluid Mech.}, Year = {2001}, Pages = {291--300}, Volume = {449}, DOI = {10.1017/S0022112001006243} } @Article{Kazantsev98, author = {E. Kazantsev}, title = {Unstable periodic orbits and attractor of the barotropic ocean model}, journal = {Nonlin. Proc. Geophys.}, year = {1998}, volume = {5}, pages = {193}, doi = {10.5194/npg-5-193-1998}, } @InCollection{Keane91, author = {Keane, M. S.}, title = {Ergodic theory and subshifts of finite type}, booktitle = {{Ergodic Theory, Symbolic Dynamics, and Hyperbolic Spaces}}, publisher = {Oxford Univ. Press}, year = {1991}, editor = {Bedford, T. and Keane, M. S. and Series, C.}, pages = {57--66}, address = {Oxford}, isbn = {9780198533900}, } @Incollection{Keating97, author = {Keating, J. P.}, title = {Resummation and the turning points of zeta functions}, booktitle = {{Classical, Semiclassical and Quantum Dynamics in Atoms}}, publisher = {Springer}, year = {1997}, editor = {B. Eckhardt and H. Friedrich}, isbn = {978-3-540-63004-3}, pages = {83--93}, address = {Berlin}, doi = {10.1007/BFb0105970}, } @Book{kellbv, title = {{Numerical Methods for Two-Point Boundary-Value Problems}}, publisher = {Dover}, year = {1992}, author = {H. B. Keller}, address = {New York}, } @InProceedings{Keller77, Title = {Numerical solution of bifurcation and nonlinear eigenvalue problems}, Author = {H. B. Keller}, Booktitle = {Applications of Bifurcation Theory}, Year = {1977}, Address = {New York}, Editor = {P. H. Rabinowitz}, Pages = {359--384}, Publisher = {Academic} } @Inproceedings{Keller79, author = {H. B. Keller}, title = {Global homotopies and {Newton} methods}, booktitle = {Recent Advances in Numerical Analysis}, year = {1979}, editor = {C. de Boor and G. H. Golub}, pages = {73--94}, address = {New York}, publisher = {Academic}, doi = {10.1016/b978-0-12-208360-0.50009-7}, } @Article{KellerEBK, author = {J. B. Keller}, title = {Corrected {Bohr--Sommerfeld} quantum conditions for nonseparable systems}, journal = {Ann. Phys. (N. Y.)}, year = {1958}, volume = {4}, pages = {180--188}, doi = {10.1016/0003-4916(58)90032-0}, } @Article{KelRug04, Title = {Eigenfunctions for smooth expanding circle maps}, Author = {G. Keller and H. H. Rugh}, Journal = {Nonlinearity}, Year = {2004}, Pages = {1723--1730}, Volume = {17}, DOI = {10.1088/0951-7715/17/5/009} } @Article{Kerswell05, Title = {Recent progress in understanding the transition to turbulence in a pipe}, Author = {R. R. Kerswell}, Journal = {Nonlinearity}, Year = {2005}, Pages = {R17--R44}, Volume = {18}, DOI = {10.1088/0951-7715/18/6/R01} } @Article{kev01ks, author = {M. E. Johnson and M. S. Jolly and I. G. Kevrekidis}, title = {The {Oseberg} transition: visualization of global bifurcations for the {Kuramoto-Sivashinsky} equation}, journal = {Int. J. Bifur. Chaos}, year = {2001}, volume = {11}, pages = {1--18}, doi = {10.1142/s0218127401001979}, } @InCollection{Khol03, author = {Kholodenko, A. L.}, booktitle = {{New Developments in String Theory Research}}, publisher = {Nova Science Publishers}, title = {Designing new apartment buildings for strings and conformal field theories. {First} steps}, year = {2006}, editor = {Grece, S. A.}, isbn = {9781594544880}, pages = {1--83}, eprint = {hep-th/0312294}, eprintclass = {hep-th}, eprinttype = {arxiv}, } @Article{Kim87, author = {J. Kim and P. Moin and R. Moser}, title = {Turbulence statistics in fully developed channel flow at low {R}eynolds number}, journal = {J. Fluid Mech.}, year = {1987}, volume = {177}, pages = {133--166}, doi = {10.1017/s0022112087000892}, } @Article{Kimball01, Title = {Chaotic properties of the soft-disk {Lorentz} gas}, Author = {Kimball, J. C.}, Journal = {Phys. Rev. E}, Year = {2001}, Pages = {066216}, Volume = {63}, DOI = {10.1103/PhysRevE.63.066216} } @Article{kirby_reconstructing_1992, author = {M. Kirby and D. Armbruster}, title = {Reconstructing phase space from {PDE} simulations}, journal = {Z. Angew. Math. Phys.}, year = {1992}, volume = {43}, pages = {999--1022}, doi = {10.1007/bf00916425}, } @Article{KirSto89, Title = {On the definition of chaos}, Author = {Kirchgraber, U. and Stoffer, D.}, Journal = {Z. Angew. Math. Mech.}, Year = {1989}, Pages = {175--185}, Volume = {69}, DOI = {10.1002/zamm.19890690703} } @Article{KirSto90, Title = {Chaotic behaviour in simple dynamical systems}, Author = {Kirchgraber, U. and Stoffer, D.}, Journal = {SIAM Rev.}, Year = {1990}, Pages = {424--452}, Volume = {32}, DOI = {10.1137/1032078} } @Article{Kirwan88, Title = {The topology of reduced phase spaces of the motion of vortices on a sphere}, Author = {Kirwan, F.}, Journal = {Physica D}, Year = {1988}, Pages = {99--123}, Volume = {30}, DOI = {10.1016/0167-2789(88)90100-5} } @Inbook{Kitchens, chapter = {Symbolic dynamics, group automorphisms and {Markov} partition}, title = {{Real and complex dynamical systems}}, publisher = {Springer}, year = {1995}, author = {B. Kitchens}, editor = {Branner, B. L. and Hjorth, P.}, volume = {464}, address = {New York}, doi = {10.1007/978-94-015-8439-5}, } @Book{Kitchens98, Title = {{Symbolic Dynamics: One-sided, Two-sided and Countable State {Markov} Shifts}}, Author = {Kitchens, B. P.}, Publisher = {Springer}, Year = {1997}, Address = {Berlin}, ISBN = {9783540627388} } @Book{KJ94, title = {{Chaos: A Program Collection for the {PC}}}, publisher = {Springer}, year = {1994}, author = {Korsch, H. J. and Jodl, H.-J.}, address = {New York}, doi = {10.1007/978-3-540-74867-0}, } @Misc{KK03, author = {K. Karamanos and I. Kotsireas}, title = {On the arithmetic nature of various constants at the accumulation points of unimodal maps and in particular of the logistic map}, year = {2003}, url = {http://docserver.carma.newcastle.edu.au/16/}, } @Inproceedings{KK05, author = {G. Kawahara and S. Kida and M. Nagata}, title = {Unstable periodic motion in plane {Couette} system: The skeleton of turbulence}, booktitle = {{One Hundred Years of Boundary Layer Research}}, year = {2005}, publisher = {Kluwer}, doi = {10.1007/978-1-4020-4150-1_40}, } @Article{KKCSG07, Title = {Fractal properties of anomalous diffusion in intermittent maps}, Author = {Korabel, N. and Klages, R. and Chechkin, A. V. and Sokolov, I. M. and Gonchar, V. Yu.}, Journal = {Phys. Rev. E}, Year = {2007}, Pages = {036213}, Volume = {75}, DOI = {10.1103/PhysRevE.75.036213} } @Article{KKGOY97, Title = {Unstable dimension variability: {A} source of nonhyperbolicity in chaotic systems}, Author = {E. J. Kostelich and I. Kan and C. Grebogi and E. Ott and J. A. Yorke}, Journal = {Physica D}, Year = {1997}, Pages = {81--90}, Volume = {109}, DOI = {10.1016/S0167-2789(97)00161-9} } @Article{KKPW89, Title = {Differentiability and analyticity of topological entropy for {Anosov} and geodesic flows}, Author = {Katok, A. and Knieper, G. and Pollicott, M. and Weiss, H.}, Journal = {Inv. Math.}, Year = {1989}, Pages = {581--597}, Volume = {98}, DOI = {10.1007/BF01393838} } @Article{Kla02, author = {Klages, R.}, journal = {Phys. Rev. E}, title = {Comment on ``{Analysis} of chaotic motion and its shape dependence in a generalized piecewise linear map''}, year = {2002}, pages = {018201}, volume = {66}, doi = {10.1103/PhysRevE.66.018201}, } @Article{Kla02a, Title = {Suppression and enhancement of diffusion in disordered dynamical systems}, Author = {Klages, R.}, Journal = {Phys. Rev. E}, Year = {2002}, Pages = {055203}, Volume = {65}, DOI = {10.1103/PhysRevE.65.055203} } @Article{KlaDor95, Title = {Simple maps with fractal diffusion coefficients}, Author = {R. Klages and J. R. Dorfman}, Journal = {Phys. Rev. Lett.}, Year = {1995}, Pages = {387--390}, Volume = {74}, DOI = {10.1103/PhysRevLett.74.387} } @Article{KlaDor97, Title = {Dynamical crossover in deterministic diffusion}, Author = {Klages, R. and Dorfman, J. R.}, Journal = {Phys. Rev. E}, Year = {1997}, Pages = {R1247--R1250}, Volume = {55}, DOI = {10.1103/PhysRevE.55.R1247} } @Article{KlaDor99, Title = {Simple deterministic dynamical systems with fractal diffusion coefficients}, Author = {Klages, R. and Dorfman, J. R.}, Journal = {Phys. Rev. E}, Year = {1999}, Pages = {5361--5383}, Volume = {59}, DOI = {10.1103/PhysRevE.59.5361} } @Article{KlaKelHow08, Title = {Continuity properties of transport coefficients in simple maps}, Author = {G. Keller and P. J. Howard and Klages, R.}, Journal = {Nonlinearity}, Year = {2008}, Pages = {1719--1743}, Volume = {21}, DOI = {10.1088/0951-7715/21/8/003} } @Article{Klein, Title = {Mandelbrot set in a non-analtytic map}, Author = {M. Klein}, Journal = {Z. Naturf. A}, Year = {1988}, Pages = {819--820}, Volume = {43}, DOI = {10.1515/zna-1988-8-916} } @Inproceedings{Kleiser80, author = {L. Kleiser and U. Schuman}, title = {Treatment of incompressibility and boundary conditions in 3-{D} numerical spectral simulations of plane channel flows}, booktitle = {{Proc. 3. GAMM Conf. Numerical Methods in Fluid Mechanics}}, year = {1980}, editor = {E. Hirschel}, pages = {165--173}, address = {Viewweg, Braunschweig}, organization = {GAMM}, doi = {10.1007/978-3-322-86146-7_17}, } @Article{KLH94, author = {G. {Kreiss} and A. {Lundbladh} and D. S. {Henningson}}, title = {Bounds for threshold amplitudes in subcritical shear flows}, journal = {J. Fluid Mech.}, year = {1994}, volume = {270}, pages = {175--198}, doi = {10.1017/s0022112094004234}, } @Article{KMOSTY10, Title = {Chaotic behavior in classical {Yang-Mills} dynamics}, Author = {Kunihiro, T. and M\"uller, B. and Ohnishi, A. and Sch\"afer, A. and Takahashi, T. T. and Yamamoto, A.}, Journal = {Phys. Rev. D}, Year = {2010}, Pages = {114015}, Volume = {82}, DOI = {10.1103/PhysRevD.82.114015} } @Article{Knauf87, author = {Knauf, A.}, title = {Ergodic and topological properties of {Coulombic} periodic potentials}, journal = {Commun. Math. Phys.}, year = {1987}, volume = {110}, pages = {89--112}, doi = {10.1007/bf01209018}, } @Article{KniKla11a, Title = {Capturing correlations in chaotic diffusion by approximation methods}, Author = {Knight, G. and Klages, R.}, Journal = {Phys. Rev. E}, Year = {2011}, Pages = {041135}, Volume = {84}, DOI = {10.1103/PhysRevE.84.041135} } @Article{KniKla11b, author = {Knight, G. and Klages, R.}, title = {Linear and fractal diffusion coefficients in a family of one-dimensional chaotic maps}, journal = {Nonlinearity}, year = {2011}, volume = {24}, pages = {227}, doi = {10.1088/0951-7715/24/1/011}, } @Article{knobloch_general_1996, author = {Knobloch, J. and Vanderbauwhede, A.}, title = {A general reduction method for periodic solutions in conservative and reversible systems}, journal = {J. Diff. Eqn.}, year = {1996}, volume = {8}, pages = {71}, doi = {10.1007/bf02218615}, } @Inproceedings{knobloch_hopf_1994, author = {Knobloch, J. and Vanderbauwhede, A.}, title = {Hopf bifurcation at k-fold resonances in equivariant reversible systems}, booktitle = {{Dynamics, Bifurcation and Symmetry, New Trends and New Tools}}, year = {1994}, editor = {P. Chossat}, pages = {167}, address = {Doredrecht}, publisher = {Kluwer}, doi = {10.1007/978-94-011-0956-7_15}, } @Article{knobloch_hopf_1996, author = {Knobloch, J. and Vanderbauwhede, A.}, title = {Hopf bifurcation at k-fold resonances in conservative systems}, journal = {Progr. Nonlinear Diff. Equations and Their Applications}, year = {1996}, volume = {19}, pages = {155--170}, doi = {10.1007/978-3-0348-7518-9_8}, } @Article{KNSks90, Title = {Back in the saddle again: a computer assisted study of the {Kuramoto-Sivashinsky} equation}, Author = {I. G. Kevrekidis and B. Nicolaenko and J. C. Scovel}, Journal = {SIAM J. Appl. Math.}, Year = {1990}, Pages = {760--790}, Volume = {50}, DOI = {10.1137/0150045} } @Book{KoFo, title = {{Elements of the Theory of Functions and Functional Analysis}}, publisher = {Dover}, year = {1980}, author = {Kolmogorov, A. N. and Fomin, S. V.}, address = {New York}, isbn = {9780486406831}, } @Article{Kongas98, author = {Kongas, O.}, title = {Stability and torsion in the period doubling cascade}, journal = {Phys. Lett. A}, year = {1998}, volume = {241}, pages = {163--167}, doi = {10.1016/s0375-9601(98)00102-9}, } @Article{kook89, Title = {Periodic orbits for reversible, symplectic mappings}, Author = {H. Kook and J. D. Meiss}, Journal = {Physica D}, Year = {1989}, Pages = {65--86}, Volume = {35}, DOI = {10.1016/0167-2789(89)90096-1} } @Article{kooknewt, author = {Kook, H.-T. and Meiss, J. D.}, journal = {Physica D}, title = {Application of {Newton}'s method to {Lagrangian} mappings}, year = {1989}, pages = {317--326}, volume = {36}, doi = {10.1016/0167-2789(89)90087-0}, } @InCollection{appendMeasure, author = {P. Cvitanovi{\'c}}, title = {Implementing evolution}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2020}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/paper.shtml#irrational}, } @Article{KoRe96, author = {Kowalski, K. and Rembielinski, J.}, title = {Groups and nonlinear dynamical systems. {Dynamics} on the {SU(2)} group}, journal = {Physica D}, year = {1996}, volume = {99}, pages = {237--251}, doi = {10.1016/s0167-2789(96)00137-6}, } @Article{KoRe98, author = {K. Kowalski and J. Rembielinski}, title = {Groups and nonlinear dynamical systems. {Chaotic} dynamics on the {SU(2)xSU(2)} group}, journal = {Chaos Solit. Fract.}, year = {1998}, volume = {9}, pages = {437--448}, doi = {10.1016/S0960-0779(97)00113-6}, } @Book{KornfeldFominSinai1982, author = {Kornfeld, I. and Fomin, S. and Sinai, Ya. G.}, publisher = {Springer}, title = {{Ergodic Theory}}, year = {1982}, address = {New York}, isbn = {978-1-4615-6929-9}, doi = {10.1007/978-1-4615-6927-5}, } @Article{Kowal87, Title = {{Hilbert} space description of classical dynamical systems {I}}, Author = {Kowalski, K.}, Journal = {Physica A}, Year = {1987}, Pages = {408--424}, Volume = {145}, DOI = {10.1016/0378-4371(87)90003-3} } @Article{Kowal88, author = {Kowalski, K.}, title = {{Hilbert} space description of classical dynamical systems {II}}, journal = {Physica A}, year = {1988}, volume = {152}, pages = {98--108}, doi = {10.1016/0378-4371(88)90066-0}, } @Article{Kowal97, author = {Kowalski, K.}, title = {Nonlinear dynamical systems and classical orthogonal polynomials}, journal = {J. Math. Phys.}, year = {1997}, volume = {38}, pages = {2483--2505}, doi = {10.1063/1.531990}, } @Article{KPR12, Title = {Resonance bifurcations of robust heteroclinic networks}, Author = {Kirk, V. and Postlethwaite, C. and Rucklidge, A.}, Journal = {SIAM J. Appl. Dyn. Sys.}, Year = {2012}, Pages = {1360--1401}, Volume = {11}, DOI = {10.1137/120864684} } @Book{Kr85, title = {{Ergodic Theorems}}, publisher = {de Gruyter}, year = {1985}, author = {U. Krengel}, address = {Berlin}, doi = {10.1515/9783110844641}, } @Incollection{KraOsi00, author = {B. Krauskopf and H. M. Osinga}, title = {Investigating torus bifurcations in the forced {Van der Pol} oscillator}, booktitle = {{Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems}}, publisher = {Springer}, year = {2000}, editor = {E. Doedel and L. Tuckerman}, isbn = {9781461212089}, pages = {199--208}, address = {New York}, doi = {10.1007/978-1-4612-1208-9_9}, } @Article{Kras04, author = {I. Krasikov and G. J. Rodgers and C. E. Tripp}, title = {Growing random sequences}, journal = {J. Phys. A}, year = {2004}, volume = {37}, pages = {2365--2370}, doi = {10.1088/0305-4470/37/6/026}, } @Article{krauskopf_survey_2005, author = {B. Krauskopf and H. M. Osinga and E. J. Doedel and M. E. Henderson and J. Guckenheimer and A. Vladimirsky and M. Dellnitz and O. Junge}, title = {A survey of methods for computing (un)stable manifolds of vector fields}, journal = {Int. J. Bifur. Chaos}, year = {2005}, volume = {15}, pages = {763--791}, doi = {10.1142/s0218127405012533}, } @Article{KraWan41, Title = {Statistics of the two-dimensional ferromagnet. {Part I}}, Author = {Kramers, H. A. and Wannier, G. H.}, Journal = {Phys. Rev.}, Year = {1941}, Pages = {252--262}, Volume = {60}, DOI = {10.1103/PhysRev.60.252} } @Article{KreEck12, Title = {Periodic orbits near onset of chaos in plane {Couette} flow}, Author = {T. Kreilos and B. Eckhardt}, Journal = {Chaos}, Year = {2012}, Pages = {047505}, Volume = {22}, DOI = {10.1063/1.4757227} } @Article{KrKrSa15, author = {Kraemer, A. S. and Kryukov, N. and Sanders, D. P.}, title = {Efficient algorithms for general periodic {Lorentz} gases in two and three dimensions}, journal = {J. Phys. A}, year = {2015}, volume = {49}, pages = {025001}, doi = {10.1088/1751-8113/49/2/025001}, } @Book{KRS08, Title = {{Anomalous Transport: Foundations and Applications}}, Author = {Klages, R. and Radons, G. and Sokolov, I. M.}, Publisher = {Wiley}, Year = {2008}, Address = {New York}, ISBN = {9783527407224} } @Article{KRSR67, author = {S. J. Kline and W. C. Reynolds and F. A. Schraub and P. W. Rundstadler}, title = {The structure of turbulent boundary layers}, journal = {J. Fluid Mech.}, year = {1967}, volume = {30}, pages = {741--773}, doi = {10.1017/s0022112067001740}, } @Article{Krupa90, Title = {Bifurcations of relative equilibria}, Author = {M. Krupa}, Journal = {{SIAM} J. Math. Anal.}, Year = {1990}, Pages = {1453--1486}, Volume = {21}, DOI = {10.1137/0521081} } @Article{KrupaRobHetCyc97, author = {M. Krupa}, journal = {J. Nonlin. Sci.}, title = {Robust heteroclinic cycles}, year = {1997}, pages = {129--176}, volume = {7}, doi = {10.1007/bf02677976}, } @Article{kruskal62, author = {M. Kruskal}, title = {Asymptotic theory of {Hamiltonian} and other systems with all solutons nearly periodic}, journal = {J. Math. Phys.}, year = {1962}, volume = {3}, pages = {806}, doi = {10.1063/1.1724285}, } @Article{kruskal65, Title = {Interaction of solitons in a collisionless plasma and the recurrence of initial states}, Author = {N. J. Zabusky and M. D. Kruskal}, Journal = {Phys. Rev. Lett.}, Year = {1965}, Pages = {240}, Volume = {15}, DOI = {10.1103/PhysRevLett.15.240} } @Article{ks05com, author = {A.-K. Kassam and L. N. Trefethen}, title = {Fourth-order time stepping for stiff {PDE}s}, journal = {SIAM J. Sci. Comput.}, year = {2005}, volume = {26}, pages = {1214--1233}, doi = {10.1137/s1064827502410633}, } @Article{kschang86, author = {H.-C. Chang}, title = {Travelling waves on fluid interfaces: {Normal} form analysis of the {Kuramoto-Sivashinsky} equation}, journal = {Phys. Fluids}, year = {1986}, volume = {29}, pages = {3142}, doi = {10.1063/1.865965}, } @Article{ksgreene88, author = {J. M. Greene and J.-S. Kim}, title = {The steady states of the {Kuramoto-Sivashinsky} equation}, journal = {Physica D}, year = {1988}, volume = {33}, pages = {99--120}, doi = {10.1016/S0167-2789(98)90013-6}, } @Article{ksgrim91, Title = {The non-existence of a certain class of travelling wave solutions of the {Kuramoto-Sivashinsky} equation}, Author = {R. Grimshaw and A. P. Hooper}, Journal = {Physica D}, Year = {1991}, Pages = {231--238}, Volume = {50}, DOI = {10.1016/0167-2789(91)90177-B} } @Article{ksham95, author = {S. Bouquet}, title = {Hamiltonian structure and integrability of the stationary {Kuramoto-Sivashinsky} equation}, journal = {J. Math. Phys.}, year = {1995}, volume = {36}, pages = {1242}, doi = {10.1063/1.531118}, } @Article{kshooper88, Title = {Travelling wave solutions of the {Kuramoto-Sivashinsky} equation}, Author = {A. P. Hooper and R. Grimshaw}, Journal = {Wave Motion}, Year = {1988}, Pages = {405--420}, Volume = {10}, DOI = {10.1016/0165-2125(88)90045-5} } @Article{kskent92, author = {P. Kent and J. Elgin}, title = {Travelling-waves of the {Kuramoto-Sivashinsky} equation: {Period-multiplying} bifurcations}, journal = {Nonlinearity}, year = {1992}, volume = {5}, pages = {899--919}, doi = {10.1088/0951-7715/5/4/004}, } @Article{kstroy89, Title = {The existence of steady solutions of the {Kuramoto-Sivashinsky} equation}, Author = {W. C. Troy}, Journal = {J. Diff. Eqn.}, Year = {1989}, Pages = {269--313}, Volume = {82}, DOI = {10.1016/0022-0396(89)90134-4} } @Article{kstroy92, Title = {Steady solutions of the {Kuramoto-Sivashinsky} equation for small wave speed}, Author = {J. Jones and W. C. Troy and A. D. MacGillivary}, Journal = {J. Diff. Eqn.}, Year = {1992}, Pages = {28--55}, Volume = {96}, DOI = {10.1016/0022-0396(92)90143-B} } @Article{ksyang97, Title = {On travelling-wave solutions of the {Kuramoto-Sivashinsky} equation}, Author = {T.-S. Yang}, Journal = {Physica D}, Year = {1997}, Pages = {25--42}, Volume = {110}, DOI = {10.1016/S0167-2789(97)00121-8} } @Article{KT84, Title = {Escape rate from strange repellers}, Author = {L. Kadanoff and C. Tang}, Journal = {Proc. Natl. Acad. Sci. USA}, Year = {1984}, Pages = {1276--1279}, Volume = {81}, DOI = {10.1073/pnas.81.4.1276} } @Article{KTH92, Title = {Pruning of orbits in four-disk and hyperbola billiards}, Author = {Hansen, K. T.}, Journal = {Chaos}, Year = {1992}, Pages = {71--75}, Volume = {2}, DOI = {10.1063/1.165900} } @Article{Kuehn11, Title = {Deterministic continutation of stochastic metastable equilibria via {Lyapunov} equations and ellipsoids}, Author = {Kuehn, C.}, Journal = {SIAM J. Sci. Comp.}, Year = {2012}, Pages = {1635--1658}, Volume = {34}, DOI = {10.1137/110839874} } @Article{KuKuKnMo04, Title = {Catastrophe theoretic classification of nonlinear oscillators}, Author = {A. Yu. Kuznetsova and A. P. Kuznetsov, C. Knudsen and E. Mosekilde}, Journal = {Int. J. Bifur. Chaos}, Year = {2004}, Pages = {1241--1266}, Volume = {12}, DOI = {10.1142/S0218127404009995} } @Book{Kunita97, author = {Kunita, H.}, publisher = {Cambridge Univ. Press}, title = {{Stochastic Flows and Stochastic Differential Equations}}, year = {1997}, address = {Cambridge UK}, isbn = {9780521599252}, } @Article{KuPa09, author = {Kuptsov, P. V. and Parlitz, U.}, title = {Strict and fussy modes splitting in the tangent space of the {Ginzburg-Landau} equation}, journal = {Phys. Rev. E}, year = {2010}, volume = {81}, pages = {036214}, doi = {10.1103/PhysRevE.81.036214}, } @Book{kura84tur, title = {{Chemical Oscillations, Waves and Turbulence}}, publisher = {Springer}, year = {1984}, author = {Y. Kuramoto}, address = {New York}, doi = {10.1007/978-3-642-69689-3}, } @Article{KurTsu76, Title = {Persistent propagation of concentration waves in dissipative media far from thermal equilibrium}, Author = {Y. Kuramoto and T. Tsuzuki}, Journal = {Progr. Theor. Phys.}, Year = {1976}, Pages = {365--369}, Volume = {55}, DOI = {10.1143/PTP.55.356} } @Article{Kus83, author = {M. Ku\v{s}}, title = {Integrals of motion for the {Lorenz} system}, journal = {J. Phys. A}, year = {1983}, volume = {16}, pages = {L689}, doi = {10.1088/0305-4470/16/18/002}, } @Article{kuturb78, author = {Y. Kuramoto}, journal = {Progr. Theor. Phys. Suppl.}, title = {Diffusion-induced chaos in reaction systems}, year = {1978}, pages = {346--367}, volume = {64}, doi = {10.1143/PTPS.64.346}, } @Book{Kuzn04, author = {Y. A. Kuznetsov}, publisher = {Springer}, title = {{Elements of Applied Bifurcation Theory}}, year = {2004}, address = {New York}, edition = {3}, isbn = {978-1-4419-1951-9}, doi = {10.1007/978-1-4757-3978-7}, } @Article{KuzOsb02, Title = {Generalized dimensions of {Feigenbaum}'s attractor from renormalization-group functional equations}, Author = {P. Kuznetsov and A. H. Osbaldestin}, Journal = {Regul. Chaotic. Dyn.}, Year = {2002}, Pages = {32--330}, Volume = {7}, DOI = {10.1070/RD2002v007n03ABEH000214} } @Article{LaChWu82, author = {Lau, S. L. and Cheung, Y. K. and Wu, S. Y.}, journal = {J. Appl. Mech.}, title = {A variable parameter incrementation method for dynamic instability of linear and nonlinear elastic systems}, year = {1982}, pages = {849--853}, volume = {49}, doi = {10.1115/1.3162626}, } @Article{LahMir99, author = {Lahme, B. and Miranda, R.}, title = {{Karhunen-Loeve} decomposition in the presence of symmetry. {I}}, journal = {IEEE Trans. Image Processing}, year = {1999}, volume = {8}, pages = {1183--1190}, doi = {10.1109/83.784431}, } @Article{LaKo89, Title = {Characterization of an experimental strange attractor by periodic orbits}, Author = {D. P. Lathrop and E. J. Kostelich}, Journal = {Phys. Rev. A}, Year = {1989}, Pages = {4028--4031}, Volume = {40}, DOI = {10.1103/PhysRevA.40.4028} } @Article{lamb_bifurcationperiodic_2003, author = {Lamb, J. S. W. and Melbourne, I. and Wulff, C.}, title = {Bifurcation from periodic solutions with spatiotemporal symmetry, including resonances and mode interactions}, journal = {J. Diff. Eqn.}, year = {2003}, volume = {191}, pages = {377--407}, doi = {10.1016/s0022-0396(03)00019-6}, } @Article{lamb98, author = {J. S. W. Lamb and J. A. G. Roberts}, title = {Time reversal symmetry in dynamical systems: {A} survey}, journal = {Physica D}, year = {1998}, volume = {112}, pages = {1--39}, doi = {10.1016/S0167-2789(97)00199-1} } @Article{Lamba04, author = {Lamba, H.}, title = {Chaotic, regular and unbounded behaviour in the elastic impact oscillator}, journal = {Physica D}, year = {1995}, volume = {82}, pages = {117--135}, doi = {10.1016/0167-2789(94)00222-C}, } @Article{LamWul02, author = {Lamb, J. S. W. and Wulff, C.}, title = {Reversible relative periodic orbits}, journal = {J. Diff. Eqn.}, year = {2002}, volume = {178}, pages = {60--100}, doi = {10.1006/jdeq.2001.4004}, } @Article{Lan11, author = {Lan, Y.}, title = {Novel computation of the growth rate of generalized random {Fibonacci} sequences}, journal = {J. Stat. Phys.}, year = {2011}, volume = {142}, pages = {847--861}, doi = {10.1007/s10955-011-0132-z}, } @Article{lanCvit07, Title = {Unstable recurrent patterns in {Kuramoto-Sivashinsky} dynamics}, Author = {Lan, Y. and Cvitanovi{\'c}, P.}, Journal = {Phys. Rev. E}, Year = {2008}, Pages = {026208}, Volume = {78}, DOI = {10.1103/PhysRevE.78.026208} } @Article{Lanczos38, author = {C. Lanczos}, title = {A remarkable property of the {Riemann-Christoffel} tensor in four dimensions}, journal = {Ann. Math. (2)}, year = {1938}, volume = {39}, pages = {842--850}, doi = {10.2307/1968467} } @Article{landau44, author = {L. D. Landau}, title = {On the problem of turbulence}, journal = {Dokl. Akad. Nauk SSSR}, year = {1944}, volume = {44}, pages = {339}, doi = {10.1016/b978-0-08-010586-4.50057-2}, } @Book{Landau59a, author = {Landau, L. D. and Lifshitz, E. M.}, publisher = {Pergamon Press}, title = {{Fluid Mechanics}}, year = {1959}, address = {Oxford}, } @Book{Landau59b, author = {Landau, L. D. and Lifshitz, E. M.}, publisher = {Pergamon Press}, title = {{Mechanics}}, year = {1959}, address = {Oxford}, edition = {3}, isbn = {978-0750628969}, url = {https://archive.org/search.php?query=creator%3A%22L.D.+Landau+%26+E.M.+Lifshitz%22}, } @Book{Landau59c, author = {Landau, L. D. and Lifshitz, E. M.}, publisher = {Pergamon Press}, title = {{Quantum Mechanics: Non-Relativistic Theory}}, year = {1959}, address = {Oxford}, isbn = {978-0750635394}, url = {https://archive.org/search.php?query=creator%3A%22L.D.+Landau+%26+E.M.+Lifshitz%22}, } @Book{Landau60, author = {Landau, L. D. and Lifshitz, E. M.}, publisher = {Pergamon Press}, title = {{Electrodynamics of Continuous Media}}, year = {1960}, address = {Oxford}, edition = {2}, isbn = {978-0750626347}, url = {https://archive.org/search.php?query=creator%3A%22L.D.+Landau+%26+E.M.+Lifshitz%22}, } @Book{Landau80a, author = {Landau, L. D. and Lifshitz, E. M.}, publisher = {Pergamon Press}, title = {{Statistical Physics, Part 1}}, year = {1980}, address = {Oxford}, isbn = {978-0750633727}, url = {https://archive.org/search.php?query=creator%3A%22L.D.+Landau+%26+E.M.+Lifshitz%22}, } @Book{Landau80b, author = {Landau, L. D. and Lifshitz, E. M.}, publisher = {Pergamon Press}, title = {{Statistical Physics, Part 2: Theory of the Condensed State}}, year = {1980}, address = {Oxford}, isbn = {978-0750626361}, url = {https://archive.org/search.php?query=creator%3A%22L.D.+Landau+%26+E.M.+Lifshitz%22}, } @Article{Landsberg2006143, Title = {The sextonions and {$E_{7 1/2}$}}, Author = {J. M. Landsberg and L. Manivel}, Journal = {Adv. Math.}, Year = {2006}, Pages = {143--179}, Volume = {201}, DOI = {10.1016/j.aim.2005.02.001} } @Article{Lanford82S, author = {{Lanford}, O. E.}, title = {A computer-assisted proof of the {Feigenbaum} conjectures}, journal = {Bull. Amer. Math. Soc.}, year = {1982}, volume = {6}, pages = {427--434}, doi = {10.1090/S0273-0979-1982-15008-X}, } @Book{Lang71, title = {{Linear Algebra}}, publisher = {Addison-Wesley}, year = {1987}, author = {S. Lang}, address = {Reading, MA}, doi = {10.1007/978-1-4757-1949-9}, } @Book{langford_normal_1995, title = {{Normal Forms and Homoclinic Chaos}}, publisher = {AMS}, year = {1995}, author = {W. F. Langford and W. Nagata}, isbn = {978-0-8218-0326-4}, doi = {10.1090/fic/004}, pages = {294}, } @Article{lanmaw03, Title = {Stationary modulated-amplitude waves in the 1{D} complex {Ginzburg-Landau} equation}, Author = {Y. Lan and N. Garnier and P. Cvitanovi{\'c}}, Journal = {Physica D}, Year = {2004}, Pages = {193--212}, Volume = {188}, DOI = {10.1016/S0167-2789(03)00289-6} } @PhdThesis{LanThesis, author = {Y. Lan}, title = {{Dynamical Systems Approach to {$1-d$} Spatiotemporal Chaos -- {A} Cyclist's View}}, school = {School of Physics, Georgia Inst. of Technology}, year = {2004}, address = {Atlanta}, url = {http://ChaosBook.org/projects/theses.html}, } @Article{lanVar1, Title = {Variational method for finding periodic orbits in a general flow}, Author = {Y. Lan and P. Cvitanovi{\'c}}, Journal = {Phys. Rev. E}, Year = {2004}, Pages = {016217}, Volume = {69}, DOI = {10.1103/PhysRevE.69.016217} } @Article{Laplace1810, Title = {M{\'e}moire sur les int{\'e}grales d{\'e}finies et leur application aux probabilit{\'e}s, et sp{\'e}cialement {\`a} la recherche du milieu qu'il faut choisir entre les r{\'e}sultats des observations}, Author = {Laplace, P. S.}, Journal = {Mem. Acad. Sci. (I), XI, Sec. V.}, Year = {1810}, Pages = {375--387}, Address = {Paris}, URL = {http://gallica.bnf.fr/ark:/12148/bpt6k77600r/f362} } @Article{laquey74, author = {R. E. LaQuey and S. M. Mahajan and P. H. Rutherford and W. M. Tang}, title = {Nonlinear saturation of the trapped-ion mode}, journal = {Phys. Rev. Lett.}, year = {1974}, volume = {34}, pages = {391--394}, doi = {10.2172/4202869}, } @Incollection{LArnold86, author = {Arnold, L. and Wihstutz, V.}, title = {{Lyapunov} exponents: a survey}, booktitle = {{Lyapunov Exponents}}, publisher = {Springer}, year = {1986}, editor = {Arnold, L. and Wihstutz, V.}, isbn = {978-3-540-39795-3}, pages = {1--26}, address = {Berlin}, doi = {10.1007/BFb0076829}, } @Article{laskar90, Title = {The chaotic behavior of the solar system: A numerical estimate of the chaotic zones}, Author = {Laskar, J.}, Journal = {Icarus}, Year = {1990}, Pages = {266--291}, Volume = {88} } @Article{LasYor77, Title = {On the existence of invariant measures for transformations with strictly turbulent trajectories}, Author = {Lasota, A. and Yorke, J. A.}, Journal = {Bull. Polish Acad. Sci. Math.}, Year = {1977}, Pages = {233--238}, Volume = {25} } @Book{latt, title = {{Quantum Fields on the Computer}}, publisher = {World Scientific}, year = {1992}, author = {M. Creutz}, isbn = {978-981-02-0940-7}, address = {Singapore}, doi = {10.1142/1634}, } @Article{lattref, author = {B. I. Henry and S. D. Watt and S. L. Wearne}, title = {A lattice refinement scheme for finding periodic orbits}, journal = {Anziam J.}, year = {2000}, volume = {42E}, pages = {C735--C751}, doi = {10.21914/anziamj.v42i0.619}, } @Book{Lau05, Title = {{Physics of Continuous Matter: Exotic and Everyday Phenomena in the Macroscopic World}}, Author = {Lautrup, B.}, Publisher = {CRC Press}, Year = {2011}, Address = {Boca Raton, FL} } @Article{lau92, Title = {The cocoon bifurcations in three-dimensional systems with two fixed points}, Author = {Y.-T. Lau}, Journal = {Int. J. Bifur. Chaos}, Year = {1992}, Pages = {543--558}, Volume = {2}, DOI = {10.1142/S0218127492000690} } @Article{LauMa74, author = {J. B. Laughlin and P. C. Martin}, title = {Transition to turbulence of a statically stressed fluid}, journal = {Phys. Rev. Lett.}, year = {1974}, volume = {33}, pages = {1189}, doi = {10.1103/physrevlett.33.1189}, } @Article{Laur91, author = {B. Lauritzen}, journal = {Phys. Rev. A}, title = {Discrete symmetries and the periodic-orbit expansions}, year = {1991}, pages = {603--606}, volume = {43}, doi = {10.1103/PhysRevA.43.603}, } @Article{Laurent-Polz04, author = {F. Laurent-Polz}, title = {Relative periodic orbits in point vortex systems}, journal = {Nonlinearity}, year = {2004}, volume = {17}, pages = {1989--2013}, doi = {10.1088/0951-7715/17/6/001}, } @InCollection{lauw86, author = {Lauwerier, H. A.}, booktitle = {{Chaos}}, publisher = {Princeton Univ. Press}, title = {One-dimensional iterative maps}, year = {1986}, address = {Princeton NJ}, editor = {Holden, A. V.}, pages = {39}, doi = {10.1515/9781400858156}, } @Article{LCC06, Title = {Variational method for locating invariant tori}, Author = {Y. Lan and C. Chandre and P. Cvitanovi{\'c}}, Journal = {Phys. Rev. E}, Year = {2006}, Pages = {046206}, Volume = {74}, DOI = {10.1103/PhysRevE.74.046206} } @Article{Leboeuf04, author = {Leboeuf, P.}, title = {Periodic orbit spectrum in terms of {Ruelle-Pollicott} resonances}, journal = {Phys. Rev. E}, year = {2004}, volume = {69}, pages = {026204}, doi = {10.1103/PhysRevE.69.026204}, } @Article{Lega_holes, author = {J. Lega}, journal = {Physica D}, title = {Traveling hole solutions of the {Complex Ginzburg-Landau} equation: a review}, year = {2001}, pages = {152--153}, volume = {269}, doi = {10.1016/s0167-2789(01)00174-9}, } @InBook{Leibniz, author = {Leibniz, G. W.}, chapter = {Von dem Verh{\"a}ngnisse}, pages = {129--134}, publisher = {Ernst Cassirer}, title = {{Hauptschriften zur Grundlegung der Philosophie}}, year = {1906}, address = {Leibzig}, } @Book{LeiRei05, author = {B. Leimkuhler and S. Reich}, publisher = {Cambridge Univ. Press}, title = {{Simulating {Hamiltonian} Dynamics}}, year = {2005}, address = {Cambridge UK}, doi = {10.1017/cbo9780511614118}, } @Article{LeTa88, author = {G. Levine and M. Tabor}, title = {Integrating the nonintegrable: analytic structure of the {Lorenz} model revisited}, journal = {Physica}, year = {1988}, volume = {33}, pages = {189--210}, doi = {10.1016/S0167-2789(98)90018-5}, } @Article{Letellier03, author = {C. Letellier}, title = {Modding out a continuous rotation symmetry for disentangling a laser dynamics}, journal = {Int. J. Bifur. Chaos}, year = {2003}, volume = {13}, pages = {1573--1577}, doi = {10.1142/s0218127403007424}, } @Book{Letellier13, Title = {{Topology and Dynamics of Chaos: In Celebration of Robert Gilmore's 70{th} Birthday}}, Author = {Letellier, C.}, Publisher = {World Scientific}, Year = {2013}, Address = {Singapore}, ISBN = {9789814434867} } @Article{LeVanQuyenMartinerieAdamEtAl1997, author = {Le Van Quyen, M. and Martinerie, J. and Adam, C. and Varela, F. J.}, journal = {Phys. Rev. E}, title = {Unstable periodic orbits in human epileptic activity}, year = {1997}, pages = {3401}, volume = {56}, doi = {10.1103/physreve.56.3401}, } @Article{Levin89, Title = {Periodic points of polynomials}, Author = {A. \'E. Eremenko and G. M. Levin}, Journal = {Ukrain. Math. J.}, Year = {1989}, Pages = {1258--1262}, Volume = {41}, DOI = {10.1007/BF01056491} } @Article{Levin91, author = {G. Levin and M. Sodin and P. Yuditskii}, title = {A {Ruelle} operator for a real {Julia} set}, journal = {Comm. Math. Phys.}, year = {1991}, volume = {141}, pages = {119--131}, doi = {10.1007/BF02100007} } @Article{Levin92, author = {G. Levin and M. Sodin and P. Yuditskii}, title = {Ruelle operators with rational weights for {Julia} sets}, journal = {J. d'Analyse Math.}, year = {1994}, volume = {63}, pages = {303}, doi = {10.1007/BF03008428} } @Article{Levin93, author = {A. Eremenko and G. Levin and M. Sodin}, title = {On the distribution of zeros of a {Ruelle} zeta-function}, journal = {Commun. Math. Phys.}, year = {1994}, volume = {159}, pages = {433}, doi = {10.1007/BF02099978} } @Article{Levin94, Title = {On {Mayer}'s conjecture and zeros of entire functions}, Author = {G. Levin}, Journal = {Ergod. Theor. Dynam. Syst.}, Year = {1994}, Pages = {565--574}, Volume = {14}, DOI = {10.1017/S0143385700008038} } @Article{lfind, author = {F. K. Diakonos and P. Schmelcher and O. Biham}, title = {Systematic computation of the least unstable periodic orbits in chaotic attractors}, journal = {Phys. Rev. Lett.}, year = {1998}, volume = {81}, pages = {4349}, doi = {10.1103/physrevlett.81.4349}, } @Book{Lichtenberg92, author = {A. J. Lichtenberg and M. A. Lieberman}, publisher = {Springer}, title = {{Regular and Chaotic Dynamics}}, year = {2013}, address = {New York}, edition = {2}, isbn = {9781475721843}, doi = {10.1007/978-1-4757-2184-3}, } @Book{liede, title = {{Applications of {Lie} Groups to Differential Equations}}, publisher = {Springer}, year = {1998}, author = {P. J. Olver}, volume = {107}, series = {GTM}, address = {New York}, doi = {10.1007/978-1-4612-4350-2}, } @InCollection{Lind96, author = {D. A. Lind}, booktitle = {{Ergodic Theory of $Z^d$ Actions}}, publisher = {Cambridge Univ. Press}, title = {A zeta function for {$Z^d$}-actions}, year = {1996}, address = {Cambridge UK}, editor = {M. Pollicott and K. Schmidt}, pages = {433--450}, doi = {10.1017/CBO9780511662812.019}, } @Book{LindMar95, author = {Lind, D. A. and Marcus, B.}, publisher = {Cambridge Univ. Press}, title = {{An Introduction to Symbolic Dynamics and Coding}}, year = {1995}, address = {Cambridge UK}, doi = {10.1017/cbo9780511626302}, } @Article{LinKS74, author = {Lin, S. P.}, title = {Finite-amplitude side-band stability of a viscous film}, journal = {J. Fluid Mech.}, year = {1974}, volume = {63}, pages = {417--429}, doi = {10.1017/s0022112074001704}, } @Unpublished{LipCvi07, author = {D. Lippolis and P. Cvitanovi{\'c}}, note = {In preparation}, title = {Optimal resolution of the state space of a chaotic flow in presence of noise}, year = {2010}, } @Article{LipCvi08, Title = {How well can one resolve the state space of a chaotic map?}, Author = {D. Lippolis and P. Cvitanovi{\'c}}, Journal = {Phys. Rev. Lett.}, Year = {2010}, Pages = {014101}, Volume = {104}, DOI = {10.1103/PhysRevLett.104.014101} } @Book{Lipkin66, title = {{Lie Groups for Pedestrians}}, publisher = {North-Holland}, year = {1966}, author = {Lipkin, H. J.}, isbn = {9780486421858}, address = {Amsterdam}, doi = {10.1016/0029-5582(66)90166-0}, } @Article{LiRe97, author = {R. G. Littlejohn and M. Reinsch}, title = {Gauge fields in the separation of rotations and internal motions in the {$n$}-body problem}, journal = {Rev. Mod. Phys.}, year = {1997}, volume = {69}, pages = {213--275}, doi = {10.1103/revmodphys.69.213}, } @Misc{liuliupego05, author = {J.-G. Liu and J. Liu and R. L. Pego}, title = {Divorcing pressure from viscosity in incompressible {Navier-Stokes} dynamics}, year = {2005}, eprint = {math.AP/0502549}, eprintclass = {math.AP}, eprinttype = {arxiv}, } @Article{Liverani01, Title = {Rigorous numerical investigation of the statistical properties of piecewise expanding maps. {A} feasibility study}, Author = {Liverani, Carlangelo}, Journal = {Nonlinearity}, Year = {2001}, Pages = {463--490}, Volume = {14}, DOI = {10.1088/0951-7715/14/3/303} } @Article{Liverani94, Title = {Decay of correlations for piecewise expanding maps}, Author = {C. Liverani}, Journal = {J. Stat. Phys.}, Year = {1995}, Pages = {1111--1129}, Volume = {78}, DOI = {10.1007/BF02183704} } @Article{LiWu87, Title = {Fast {Galerkin} method and its application to determine periodic solutions of non-linear oscillators}, Author = {F. H. Ling and X. X. Wu}, Journal = {Int. J. Non-Linear Mechanics}, Year = {1987}, Pages = {89 --98}, Volume = {22}, DOI = {10.1016/0020-7462(87)90012-6} } @InCollection{Llibre15, author = {Llibre, J.}, booktitle = {{Central Configurations, Periodic Orbits, and Hamiltonian Systems}}, publisher = {Springer}, title = {The averaging theory for computing periodic orbits}, year = {2015}, address = {Basel}, pages = {1--104}, series = {Advanced Courses in Mathematics - CRM Barcelona}, doi = {10.1007/978-3-0348-0933-7_1}, } @Book{lls, Title = {{Systems of Quasilinear Equations and Their Applications to Gas Dynamics}}, Author = {B. L. Ro\v{z}destvenski\v{i} and N. N. Janenko}, Publisher = {AMS}, Year = {1983}, Address = {Providence, RI} } @Article{LM86, Title = {Numerical study of a billiard in a gravitational field}, Author = {H. E. Lehtihet and B. N. Miller}, Journal = {Physica D}, Year = {1986}, Pages = {93--104}, Volume = {21}, DOI = {10.1016/0167-2789(86)90080-1} } @Book{LM94, title = {{Chaos, Fractals, and Noise; Stochastic Aspects of Dynamics}}, publisher = {Springer}, year = {1994}, author = {A. Lasota and M. MacKey}, address = {New York}, isbn = {9781461242864} } @Article{LNRM94, Title = {The nonequilibrium {Lorentz} gas}, Author = {J. Lloyd and M. Niemeyer and L. Rondoni and G. P. Morriss}, Journal = {Chaos}, Year = {1995}, Pages = {536--551}, Volume = {5}, DOI = {10.1063/1.166139} } @Mastersthesis{Lomb, Author = {R. Lombardi}, School = {Universit{\'a} degli studi di Milano}, Year = {1993}, Note = {Laurea thesis} } @Article{lop05rel, author = {V. L{\'o}pez and P. Boyland and M. T. Heath and R. D. Moser}, title = {Relative periodic solutions of the {Complex Ginzburg-Landau} equation}, journal = {SIAM J. Appl. Dyn. Syst.}, year = {2006}, volume = {4}, pages = {1042}, doi = {10.1137/040618977}, } @Misc{lopezLink, author = {Vanessa L{\'o}pez}, note = {Private communication}, } @Article{Lorentz1905, Title = {The motion of electrons in metallic bodies}, Author = {Lorentz, H. A.}, Journal = {K. Ned. Akad. van Wet. B}, Year = {1905}, Pages = {438--453}, Volume = {7}, URL = {http://www.dwc.knaw.nl/DL/publications/PU00013989.pdf} } @Article{LorentzDiff, Title = {Transport properties of the {Lorentz} gas in terms of periodic orbits}, Author = {Cvitanovi{\'c}, P. and Eckmann, J.-P. and Gaspard, P.}, Journal = {Chaos Solit. Fract.}, Year = {1995}, Pages = {113--120}, Volume = {6}, DOI = {10.1016/0960-0779(95)80018-C} } @Article{lorenz, Title = {Deterministic nonperiodic flow}, Author = {E. N. Lorenz}, Journal = {J. Atmos. Sci.}, Year = {1963}, Pages = {130--141}, Volume = {20}, DOI = {10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2} } @Article{Lorenz60, Title = {Maximum simplification of the dynamics equations}, Author = {E. N. Lorenz}, Journal = {Quart. J. Geophys.}, Year = {1960}, Pages = {243--254}, Volume = {12}, DOI = {10.1111/j.2153-3490.1960.tb01307.x} } @Article{Lorenz63a, Title = {The mechanics of vacillation}, Author = {E. N. Lorenz}, Journal = {J. Meteorology}, Year = {1963}, Pages = {448--465}, Volume = {20}, DOI = {10.1175/1520-0469(1963)020<0448:TMOV>2.0.CO;2} } @Article{Lorenz65, Title = {A study of the predictability of a 28-variable atmospheric model}, Author = {Lorenz, E. N.}, Journal = {Tellus}, Year = {1965}, Pages = {321--333}, Volume = {17}, DOI = {10.1111/j.2153-3490.1965.tb01424.x} } @Article{lorenz69, Title = {The predictability of a flow which possesses many scales of motion}, Author = {E. N. Lorenz}, Journal = {Tellus}, Year = {1969}, Pages = {289--307}, Volume = {21}, DOI = {10.1111/j.2153-3490.1969.tb00444.x} } @Article{Lorenz84, Title = {Irregularity: a fundamental property of the atmosphere}, Author = {Lorenz, E. N.}, Journal = {Tellus A}, Year = {1984}, Pages = {98--110}, Volume = {36}, DOI = {10.1111/j.1600-0870.1984.tb00230.x} } @Article{LoTh10, author = {G. J. Lord and V. Th\"ummler}, title = {Freezing stochastic travelling waves}, journal = {SIAM J. Sci. Comput.}, year = {2012}, volume = {34}, pages = {B24--B43}, doi = {10.1137/100784734}, } @Article{Low58, author = {F. E. Low}, title = {A {Lagrangian} formulation of the {Boltzmann-Vlasov} equation for plasmas}, journal = {Proc. R. Soc. Lond. A}, year = {1958}, volume = {248}, pages = {282--287}, doi = {10.1098/rspa.1958.0244}, } @Article{lozi2, Title = {Un attracteur {{\'e}}trange (?) du type attracteur de {H{\'e}non}}, Author = {R. Lozi}, Journal = {J. Phys. (Paris) Colloq.}, Year = {1978}, Pages = {C5--C9}, Volume = {39}, DOI = {10.1051/jphyscol:1978505} } @Article{LP80, Title = {The semiclassical two-electron atom and the old quantum theory}, Author = {J. G. Leopold and I. Percival}, Journal = {J. Phys. B}, Year = {1980}, Pages = {1037}, Volume = {13}, DOI = {10.1088/0022-3700/13/6/012} } @Article{LPKDS09, Title = {Evolutionary phase space in driven elliptical billiards}, Author = {F. Lenz and C. Petri and F. N. R. Koch and F. K. Diakonos and P. Schmelcher}, Journal = {New J. Phys.}, Year = {2009}, Pages = {083035}, Volume = {11}, DOI = {10.1088/1367-2630/11/8/083035} } @Article{LPPS01, Title = {Quantum correlations and classical resonances in an open chaotic system}, Author = {Lu, W. T. and K. Prance and P. Pradhan and S. Sridhar}, Journal = {Physica Scripta}, Year = {2001}, Pages = {238}, Volume = {2001}, DOI = {10.1088/0031-8949/2001/T90/034} } @Article{LRM94, Title = {The breakdown of ergodic behaviour in the {Lorentz} gas}, Author = {J. Lloyd and L. Rondoni and G. P. Morriss}, Journal = {Phys. Rev. E}, Year = {1994}, Pages = {3416}, Volume = {50}, DOI = {10.1103/PhysRevE.50.3416} } @Article{lsy-lozi, Title = {{Bowen-Ruelle} measures for certain piecewise hyperbolic maps}, Author = {L.-S. Young}, Journal = {Trans. Amer. Math. Soc.}, Year = {1985}, Pages = {41--48}, Volume = {287}, DOI = {10.2307/2000396} } @Article{LT06, Title = {Zeta functions and dynamical systems}, Author = {C. Liverani and M. Tsujii}, Journal = {Nonlinearity}, Year = {2006}, Pages = {2467}, Volume = {19}, DOI = {10.1088/0951-7715/19/10/011} } @Article{LucDoe1993, author = {{Luce}, B. P. and {Doering}, C. R.}, title = {Scaling of turbulent spike amplitudes in the complex {Ginzburg-Landau} equation}, journal = {Phys. Lett. A}, year = {1993}, volume = {178}, pages = {92--98}, doi = {10.1016/0375-9601(93)90733-g}, } @Article{Luce95, author = {B. P. Luce}, title = {Homoclinic explosions in the complex {Ginzburg-Landau} equation}, journal = {Physica D}, year = {1995}, volume = {84}, pages = {553--581}, doi = {10.1016/0167-2789(95)00047-8}, } @Article{Luck, Title = {Bouncing ball with a finite restitution: {Chattering} locking, and chaos}, Author = {J. M. Luck and A. Mehta}, Journal = {Phys. Rev. E}, Year = {1993}, Pages = {3988}, Volume = {48}, DOI = {10.1103/PhysRevE.48.3988} } @Article{LundJohan91, author = {A. Lundbladh and A. Johansson}, title = {Direct simulation of turbulent spots in plane {Couette} flow}, journal = {J. Fluid Mech.}, year = {1991}, volume = {229}, pages = {499--516}, doi = {10.1017/s0022112091003130}, } @Article{LuPi09, author = {Lu{\'e}vano, J.-R. and Pina, E.}, title = {The {Schr{\"o}der} functional equation and its relation to the invariant measures of chaotic maps}, journal = {J. Phys. A.}, year = {2008}, volume = {41}, pages = {265101}, doi = {10.1088/1751-8113/41/26/265101} } @Article{Lust01, Title = {Improved numerical {Floquet} multipliers}, Author = {K. Lust}, Journal = {Int. J. Bifur. Chaos}, Year = {2001}, Pages = {2389--2410}, Volume = {11}, DOI = {10.1142/S0218127401003486} } @Article{Lutzky88, author = {Lutzky, M.}, journal = {Phys. Lett. A}, title = {Counting stable cycles in unimodal iterations}, year = {1988}, pages = {248--250}, volume = {131}, doi = {10.1016/0375-9601(88)90021-7}, } @Article{Lutzky93, author = {Lutzky, M.}, journal = {Phys. Lett. A}, title = {Counting hyperbolic components of the {Mandelbrot} set}, year = {1993}, pages = {338--340}, volume = {177}, doi = {10.1016/0375-9601(93)90011-N}, } @Article{LuZeSr06, Title = {Duality between quantum and classical dynamics for integrable billiards}, Author = {Lu, W. T. and Zeng, W. and Sridhar, S.}, Journal = {Phys. Rev. E}, Year = {2006}, Pages = {046201}, Volume = {73}, DOI = {10.1103/PhysRevE.73.046201} } @Article{LVPRS00, Title = {Microwave study of quantum n-disk scattering}, Author = {Lu, W. and Viola, L. and Pance, K. and Rose, M. and Sridhar, S.}, Journal = {Phys. Rev. E}, Year = {2000}, Pages = {3652--3663}, Volume = {61}, DOI = {10.1103/PhysRevE.61.3652} } @Article{lyaos, Title = {A multiplicative ergodic theorem. {Liapunov} characteristic numbers for dynamical systems}, Author = {V. I. Oseledec}, Journal = {Trans. Moscow Math. Soc.}, Year = {1968}, Pages = {197--221}, Volume = {19}, URL = {http://mi.mathnet.ru/eng/mmo214} } @Article{Lyapunov1892, Title = {Probl\`eme g{\'e}n{\'e}ral de la stabilit{\'e} du mouvement}, Author = {A. Lyapunov}, Journal = {Ann. Math. Studies}, Year = {1977}, Note = {Russian original Kharkow, 1892}, Pages = {531--534}, Volume = {17} } @Article{Lyapunov1892en, Title = {The general problem of the stability of motion}, Author = {A. M. Lyapunov}, Journal = {Int. J. Control}, Year = {1992}, Pages = {531--534}, Volume = {55}, DOI = {10.1080/00207179208934253} } @Book{Lyn85, author = {R. C. Lyndon}, publisher = {Cambridge Univ. Press}, title = {{Groups and Geometry}}, year = {1985}, address = {Cambridge UK}, doi = {10.1017/cbo9781107325685}, } @Book{lyschm, title = {{{Lyapunov-Schmidt} Methods in Nonlinear Analysis and Applications}}, publisher = {Kluwer}, year = {2002}, author = {N. Sidorov and B. Loginov and A. Sinitsyn and M. Falaleev}, address = {Dordrecht}, doi = {10.1007/978-94-017-2122-6}, } @Article{M86, author = {Maslowe, S. A.}, journal = {Ann. Rev. Fluid Mech.}, title = {Critical layers in shear flows}, year = {1986}, pages = {405--432}, volume = {18}, doi = {10.1146/annurev.fluid.18.1.405}, } @Article{MacKay, author = {R. S. MacKay and I. C. Percival}, title = {Universal small-scale structure near the boundary of {Siegel} disks of arbitrary rotation number}, journal = {Physica D}, year = {1987}, volume = {26}, pages = {193--202}, doi = {10.1016/0167-2789(87)90223-5} } @Article{MacKay1, author = {R. S. MacKay}, title = {Flux over a saddle}, journal = {Phys. Lett. A}, year = {1990}, volume = {145}, pages = {425}, doi = {10.1016/0375-9601(90)90306-9}, } @Article{MACKAY198499, author = {R. S. MacKay}, title = {Equivariant universality classes}, journal = {Phys. Lett. A}, year = {1984}, volume = {106}, pages = {99--100}, doi = {10.1016/0375-9601(84)90897-1}, } @Article{MacKay2, author = {R. S. MacKay}, title = {A variational principle for invariant odd-dimensional submanifolds of an energy surface for {Hamiltonian} systems}, journal = {Nonlinearity}, year = {1991}, volume = {4}, pages = {155}, doi = {10.1088/0951-7715/4/1/010}, } @Article{MacKay84, author = {R. S. MacKay}, title = {Equivariant universality classes}, journal = {Phys. Lett. A}, year = {1984}, volume = {106}, pages = {99--100}, doi = {10.1016/0375-9601(84)90897-1} } @Article{mackay92, author = {R. S. MacKay and J. D. Meiss}, title = {Cantori for symplectic maps near the anti-integrable limit}, journal = {Nonlinearity}, year = {1992}, volume = {5}, pages = {149--160}, doi = {10.1088/0951-7715/5/1/006}, } @Article{MacZwa83, Title = {Diffusion in a periodic {Lorentz} gas}, Author = {Machta, J. and Zwanzig, R.}, Journal = {Phys. Rev. Lett.}, Year = {1983}, Pages = {1959--1962}, Volume = {50}, DOI = {10.1103/PhysRevLett.50.1959} } @Book{MaGu04, title = {{Problems and Solutions in Group Theory for Physicists}}, publisher = {World Scientific}, year = {2004}, author = {Ma, Z. Q. and Gu, X. Y.}, isbn = {9789812388339}, doi = {10.1142/9789812562418}, } @Article{Mahm92, Title = {On periodic orbits of nonlinear dynamical systems with many degrees of freedom}, Author = {G. M. Mahmoud}, Journal = {Physica A}, Year = {1992}, Pages = {385--395}, Volume = {181}, DOI = {10.1016/0378-4371(92)90095-8} } @Article{mahmoud08a, author = {Mahmoud, G. M. and Ahmed, M. E. and Mahmoud, E. E.}, title = {Analysis of hyperchaotic complex {Lorenz} systems}, journal = {Int. J. Mod. Phys. C}, year = {2008}, volume = {19}, pages = {1477--1494}, doi = {10.1142/s0129183108013151}, } @Article{mahmoud08b, author = {Mahmoud, G.l M. and Al-Kashif, M. A. and Farghaly, A. A.}, title = {Chaotic and hyperchaotic attractors of a complex nonlinear system}, journal = {J. Phys. A}, year = {2008}, volume = {41}, doi = {10.1088/1751-8113/41/5/055104}, } @Article{mahmoud09, author = {Mahmoud, G. M. and Bountis, T. and Al-Kashif, M. A. and Aly, S. A.}, title = {Dynamical properties and synchronization of complex non-linear equations for detuned lasers}, journal = {Dyn. Systems-Internat. J.}, year = {2009}, volume = {24}, pages = {63--79}, doi = {10.1080/14689360802438298}, } @PhdThesis{Mainieri_thesis, author = {Mainieri, R.}, title = {{Thermodynamic zeta functions for {Ising} models with long-range interactions}}, school = {Physics Dept., New York Univ.}, year = {1990}, } @Article{Mainieri92a, author = {R. Mainieri}, title = {Thermodynamic zeta functions for {Ising} models with long-range interactions}, journal = {Phys. Rev. A}, year = {1992}, volume = {45}, pages = {3580--3591}, doi = {10.1103/physreva.45.3580}, } @Article{Mainieri92b, author = {R. Mainieri}, title = {Zeta function for the {Lyapunov} exponent of a product of random matrices}, journal = {Phys. Rev. Lett.}, year = {1992}, volume = {68}, pages = {1965--1968}, doi = {10.1103/PhysRevLett.68.1965}, } @Misc{Mainieri95, author = {Mainieri, R.}, title = {Geometrization of spin systems using cycle expansions}, year = {1995}, url = {http://arxiv.org/abs/chao-dyn/9502023}, } @Book{man90b, title = {{Dissipative Structures and Weak Turbulence}}, publisher = {Academic}, year = {1990}, author = {Manneville, P.}, address = {New York}, } @Book{mandel, title = {{The Fractal Geometry of Nature}}, publisher = {Freeman}, year = {1982}, author = {B. B. Mandelbrot}, isbn = {9780716711865}, address = {San Francisco}, doi = {10.1119/1.13295}, } @Book{Manin07, Title = {{Mathematics as Metaphor: Selected Essays}}, Author = {Manin, Yu. I.}, Publisher = {Amer. Math. Soc.}, Year = {2007}, ISBN = {9780821843314} } @Article{Mann04, author = {P. Manneville}, title = {Spots and turbulent domains in a model of transitional plane {Couette} flow}, journal = {Theor. Comp. Fluid Dyn.}, year = {2004}, volume = {18}, pages = {169--181}, doi = {10.1007/s00162-004-0142-4}, } @Book{Manneville04, title = {{Instabilities, Chaos and Turbulence: An Introduction to Nonlinear Dynamics and Complex Systems}}, publisher = {Imperial College Press}, year = {2004}, author = {Manneville, P.}, doi = {10.1142/p349}, } @Article{manning, Title = {{Axiom A} diffeomorphisms have rational zeta function}, Author = {A. Manning}, Journal = {Bull. London Math. Soc.}, Year = {1971}, Pages = {215--220}, Volume = {3}, DOI = {10.1112/blms/3.2.215} } @Article{Manton, author = {N. S. Manton and M. Nauenberg}, title = {Universal scaling bahavior for iterated maps in the complex plane}, journal = {Comm. Math. Phys.}, year = {1983}, volume = {89}, pages = {555--570}, doi = {10.1007/bf01214743}, } @Article{MaPo80, Title = {Different ways to turbulence in dissipative dynamical systems}, Author = {Manneville, P. and Pomeau, Y.}, Journal = {Physica D}, Year = {1980}, Pages = {219-- 226}, Volume = {1}, DOI = {10.1016/0167-2789(80)90013-5} } @Article{MaRi83, author = {{Maxey}, M. R. and {Riley}, J. J.}, title = {Equation of motion for a small rigid sphere in a nonuniform flow}, journal = {Phys. Fluids}, year = {1983}, volume = {26}, pages = {883--889}, doi = {10.1063/1.864230}, } @Article{MarLopBla04, Title = {Bifurcations in systems with {Z2} spatio-temporal and {O(2)} spatial symmetry}, Author = {F. Marques and J. M. Lopez and H. M. Blackburn}, Journal = {Physica D}, Year = {2004}, Pages = {247--276}, Volume = {189}, DOI = {10.1016/j.physd.2003.09.041} } @Article{MaRoLa02, Title = {Partial reduction in the {N}-body planetary problem using the angular momentum integral}, Author = {Malige, F. and Robutel, P. and Laskar, J.}, Journal = {Celestial Mech. Dynam. Astronom.}, Year = {2002}, Pages = {283--316}, Volume = {84}, DOI = {10.1023/A:1020392219443} } @Book{MarRat99, title = {{Introduction to Mechanics and Symmetry}}, publisher = {Springer}, year = {1999}, author = {Marsden, J. E. and Ratiu, T. S.}, address = {New York}, doi = {10.1007/978-0-387-21792-5}, } @Book{Marsd92, author = {Marsden, J. E.}, publisher = {Cambridge Univ. Press}, title = {{Lectures on Mechanics}}, year = {1992}, address = {Cambridge UK}, doi = {10.1017/cbo9780511624001}, } @Book{marsden_hamiltonian_2007, author = {Marsden, J. E. and Misiolek, G. and Ortega, J.-P. and Perlmutter, M. and Ratiu, T. S.}, publisher = {Springer}, title = {{Hamiltonian Reduction by Stages}}, year = {1964}, address = {New York}, } @Book{marsdenbb, title = {{The {Hopf} Bifurcation and its Applications}}, publisher = {Springer}, year = {1976}, author = {J. E. Marsden and M. McCracken}, isbn = {978-1-4612-6374-6}, address = {New York}, doi = {10.1007/978-1-4612-6374-6}, } @Article{MarStr08, Title = {Kinetic transport in the two-dimensional periodic {Lorentz} gas}, Author = {J. Marklof and A. Str{\"{o}}mbergsson}, Journal = {Nonlinearity}, Year = {2008}, Pages = {1413}, Volume = {21}, DOI = {10.1088/0951-7715/21/7/001} } @Article{MarStr11, Title = {The periodic {Lorentz} gas in the {Boltzmann-Grad} limit: asymptotic estimates}, Author = {Marklof, J. and Str{\"{o}}mbergsson, A.}, Journal = {Geom. Funct. Anal.}, Year = {2011}, Pages = {560--647}, Volume = {21}, DOI = {10.1007/s00039-011-0116-9} } @Article{MarStr14, Title = {Power-law distributions for the free path length in {Lorentz} gases}, Author = {Marklof, J. and Str{\"{o}}mbergsson, A.}, Journal = {J. Stat. Phys.}, Year = {2014}, Pages = {1072--1086}, Volume = {155}, DOI = {10.1007/s10955-014-0935-9} } @Article{mart87lfa, author = {C. C. Martens and M. J. Davis and G. S. Ezra}, title = {Local frequency analysis of chaotic motion in multidimensional systems: energy transport and bottlenecks in planar {OCS}}, journal = {Chem. Phys. Lett.}, year = {1987}, volume = {142}, pages = {519}, doi = {10.1016/0009-2614(87)80655-3}, } @Article{Marw08, author = {N. Marwan}, title = {A historical review of recurrence plots}, journal = {Eur. Phys. J.}, year = {2008}, volume = {164}, pages = {3--12}, doi = {10.1140/epjst/e2008-00829-1}, } @Article{MaSaTAS81, author = {S. G. Matanyan and G. K. Savvidy and N. G. Ter-Arutyunyan-Savvidy}, title = {Classical {Yang-Mills} mechanics. {Nonlinear} colour oscillations}, journal = {Sov. Phys. JETP}, year = {1981}, volume = {80}, pages = {830--838}, url = {http://www.jetp.ac.ru/cgi-bin/dn/e_053_03_0421.pdf}, } @Article{MaSiRo73, Title = {Statistical mechanics of classical systems}, Author = {Martin, P. C. and Siggia, E. D. and Rose, H. A.}, Journal = {Phys. Rev. A}, Year = {1973}, Pages = {423--437}, Volume = {8}, DOI = {10.1103/PhysRevA.8.423} } @Article{MaSkAn11, Title = {Probing the local dynamics of periodic orbits by the generalized alignment index {(GALI)} method}, Author = {{Manos}, T. and {Skokos}, C. and {Antonopoulos}, C.}, Journal = {Int. J. Bifur. Chaos}, Year = {2012}, Pages = {1250218}, Volume = {22}, DOI = {10.1142/S0218127412502185} } @Misc{Mathar10, author = {Mathar, R. J.}, title = {{Chebyshev} series representation of {Feigenbaum's} period-doubling function}, year = {2010}, eprint = {1008.4608}, eprinttype = {arxiv}, } @Article{Mather91, author = {J. N. Mather}, title = {Variational construction of orbits of twist difeomorphisms}, journal = {J. Am. Math. Soc.}, year = {1991}, volume = {4}, pages = {207--263}, doi = {10.2307/2939275}, } @Article{Mathieu68, Title = {M{\'e}moire sur le mouvement vibratoire d'une membrane de forme elliptique}, Author = {Mathieu, E.}, Journal = {J. Math. Pures Appl.}, Year = {1868}, Pages = {137--203}, Volume = {13} } @Book{MathWalk73, title = {{Mathematical Methods of Physics}}, publisher = {W. A. Benjamin}, year = {1970}, author = {J. Mathews and R. L. Walker}, isbn = {9780805370027}, address = {Reading, MA}, doi = {10.2307/2316002}, } @Misc{mwGrOrtThe, author = {Weisstein, E. W.}, title = {Group orthogonality theorem}, year = {2012}, publisher = {Wolfram MathWorld}, url = {http://mathworld.wolfram.com/GroupOrthogonalityTheorem.html} } @Misc{mathwFeigF, Title = {Feigenbaum function}, Author = {Weisstein, E. W.}, Year = {2012}, Publisher = {Wolfram MathWorld}, URL = {http://mathworld.wolfram.com/FeigenbaumFunction.html} } @Article{Matyas, Title = {Irregular diffusion in the bouncing ball billiard}, Author = {L. Matya{\'s} and R. Klages}, Journal = {Physica D}, Year = {2004}, Pages = {165}, Volume = {187}, DOI = {10.1016/j.physd.2003.09.008} } @Article{MaWaRe89, Title = {Classical, semiclassical, and quantum mechanics of a globally chaotic system: {I}ntegrability in the adiabatic approximation}, Author = {C. C. Martens and R. L. Waterland and W. P. Reinhardt}, Journal = {J. Chem. Phys.}, Year = {1989}, Pages = {2328}, Volume = {90}, DOI = {10.1063/1.455974} } @Article{MaWe74, Title = {Reduction of symplectic manifolds with symmetry}, Author = {Marsden, J. E. and Weinstein, A.}, Journal = {Rep. Math. Phys.}, Year = {1974}, Pages = {121--30}, Volume = {5}, DOI = {10.1016/0034-4877(74)90021-4} } @Article{May76, Title = {Simple mathematical models with very complicated dynamics}, Author = {May, R. M.}, Journal = {Nature}, Year = {1976}, Pages = {459--467}, Volume = {261}, DOI = {10.1038/261459a0} } @Article{Mayer76, Title = {On a {$\zeta$} function related to the continued fraction transformation}, Author = {D. H. Mayer}, Journal = {Bull. Soc. Math. Fr.}, Year = {1976}, Pages = {195--203}, Volume = {104}, URL = {http://www.numdam.org/item?id=BSMF_1976__104__195_0} } @Book{Mayer80, title = {{The Ruelle-Araki Transfer Operator in Classical Statistical Mechanics}}, publisher = {Springer}, year = {1980}, author = {Mayer, D. H.}, isbn = {9783662186497}, address = {Berlin}, doi = {10.1007/bfb0017919}, } @InCollection{Mayer91, author = {D. H. Mayer}, booktitle = {{Ergodic Theory, Symbolic Dynamics, and Hyperbolic Spaces}}, publisher = {Oxford Univ. Press}, title = {Continued fractions and related transformations}, year = {1991}, address = {Oxford}, editor = {Bedford, T. and Keane, M. S. and Series, C.}, isbn = {9780198533900}, } @Article{MayRoe87, author = {Mayer, D. and Roepstorff, G.}, title = {On the relaxation time of {Gauss}'s continued-fraction map {I. The Hilbert} space approach {(Koopmanism)}}, journal = {J. Stat. Phys.}, year = {1987}, volume = {47}, pages = {149--171}, doi = {10.1007/BF01009039}, } @Article{MC96pha, author = {Manneville, P. and Chat{\'e}, H.}, title = {Phase turbulence in the two-dimensional complex {Ginzburg-Landau} equation}, journal = {Physica D}, year = {1996}, volume = {96}, pages = {30--46}, doi = {10.1016/0167-2789(96)00045-0}, abtract = {instability of plane waves}, } @InProceedings{McCordMontaldi, author = {C. McCord AND J. Montaldi AND M. Roberts AND L. Sbano}, booktitle = {Proc. {Equadiff 2003}}, title = {Relative periodic orbits of symmetric {Lagrangian} systems}, year = {2004}, editor = {F. Dumortier and et.al.}, pages = {482--493}, doi = {10.1142/9789812702067_0078}, url = {https://www.researchgate.net/profile/James_Montaldi/publication/228539273_Relative_periodic_orbits_of_symmetric_Lagrangian_systems/links/0912f50adde3244c1d000000.pdf}, } @Unpublished{McICvi15, Title = {Periodic orbit theory of linear response}, Author = {B. McInroe and P. Cvitanovi{\'c}}, Note = {In preparation}, Year = {2016} } @Article{McKean74, author = {McKean, H. P.}, title = {Selberg's trace formula as applied to a compact {Riemann} surface}, journal = {Commun. Pure Appl. Math.}, year = {1972}, volume = {25}, pages = {225--246}, doi = {10.1002/cpa.3160250302} } @Article{McKeon04, author = {B. J. McKeon and J. Li and W. Jiang and J. F. Morrison and A. J. Smits}, title = {Further observations on the mean velocity in fully-developed pipe flow}, journal = {J. Fluid Mech.}, year = {2004}, volume = {501}, pages = {135--147}, doi = {10.1017/S0022112003007304}, } @PhdThesis{McLellan12, author = {McLellan, K. A.}, school = {Dalhousie Univ.}, title = {{Periodic Coefficients and Random {Fibonacci} Sequences}}, year = {2012}, address = {Halifax, Nova Scotia}, url = {http://hdl.handle.net/10222/15381}, } @PhdThesis{mclellan2012periodic, author = {McLellan, K. A.}, title = {{Periodic Coefficients and Random Fibonacci Sequences}}, school = {Dalhousie Univ.}, year = {2012}, url = {http://hdl.handle.net/10222/15381}, } @Book{McM94, Title = {{Complex Dynamics and Renormalization}}, Author = {McMullen, C. T.}, Publisher = {Princeton Univ. Press}, Year = {1994}, ISBN = {9781400882557} } @Article{Mcoh03, author = {M. van Hecke}, title = {Coherent and incoherent structures in systems described by the 1{D cGLe}: {Experiments} and identification}, journal = {Physica D}, year = {2003}, volume = {174}, pages = {134}, doi = {10.1016/s0167-2789(02)00687-5}, } @Article{mcord86, author = {C. K. McCord}, title = {Uniqueness of connection orbits in the equation {$y^{(3)}=y^2-1$}}, journal = {J. Math. Anal. Appl.}, year = {1986}, volume = {114}, pages = {584--592}, url = {http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2&doc=GetTRDoc.pdf&AD=ADA139261}, } @Article{mechta, author = {J. Mechta}, title = {Power law decay of correlations in a billiard problem}, journal = {J. Stat. Phys.}, year = {1983}, volume = {33}, pages = {555}, doi = {10.1007/bf01008956}, } @Book{meer_hamiltonian_1994, author = {van der Meer, J. C. and Sanders, J. A. and Vanderbauwhede, A.}, publisher = {Eindhoven Univ. of Technology, Dept. of Math. and Comp. Sci.}, title = {{Hamiltonian Structure of the Reversible Nonsemisimple 1:1 Resonance}}, year = {1994}, address = {Eindhoven}, series = {Reports on applied and numerical analysis, RANA 94-02}, doi = {10.1007/978-94-011-0956-7_19}, } @Book{Mees81, title = {{Dynamics of Feedback Systems}}, publisher = {Wiley}, year = {1981}, author = {Mees, A. I.}, address = {New York}, } @Article{MEF04, author = {J. Moehlis and B. Eckhardt and H. Faisst}, title = {Fractal lifetimes in the transition to turbulence}, journal = {Chaos}, year = {2004}, volume = {14}, pages = {S11}, doi = {10.1063/1.1821751}, } @Book{Mehta, title = {{Random Matrices}}, publisher = {Academic}, year = {2004}, author = {M. L. Mehta}, address = {New York}, isbn = {9780080474113}, } @Article{Mei08, author = {J. D. Meiss}, title = {Visual explorations of dynamics: {The} standard map}, journal = {Pramana, Indian Acad. Sci.}, year = {2008}, volume = {70}, pages = {965--988}, doi = {10.1007/s12043-008-0103-3}, } @Article{Mein95s, author = {G. Meinsma}, title = {Elementary proof of the {Routh-Hurwitz} test}, journal = {Systems and Control Lett.}, year = {1995}, volume = {25}, pages = {237--242}, doi = {10.1016/0167-6911(94)00089-E}, } @Article{meiss92, Title = {Symplectic maps, variational principles, and transport}, Author = {J. D. Meiss}, Journal = {Rev. Mod. Phys.}, Year = {1992}, Pages = {795--848}, Volume = {64}, DOI = {10.1103/RevModPhys.64.795} } @Book{Meisso7, title = {{Differential Dynamical Systems}}, publisher = {SIAM}, year = {2007}, author = {J. D. Meiss}, isbn = {9780898716351}, address = {Philadelphia}, doi = {10.1137/1.9780898718232}, } @Article{Mendoza13a, author = {Valent{\'{i}}n Mendoza}, title = {Proof of the {Pruning Front Conjecture} for certain {H{\'e}non} parameters}, journal = {Nonlinearity}, year = {2013}, volume = {26}, pages = {679}, doi = {10.1088/0951-7715/26/3/679} } @Article{Mendoza13b, author = {Mendoza, V.}, title = {A note about pruning and {H{\'e}non} maps}, journal = {Qual. Theory Dyn. Syst.}, year = {2013}, volume = {12}, pages = {443--448}, doi = {10.1007/s12346-013-0101-9}, } @Article{Mermin92, Title = {The space groups of icosahedral quasicrystals and cubic, orthorhombic, monoclinic, and triclinic crystals}, Author = {Mermin, N. D.}, Journal = {Rev. Mod. Phys.}, Year = {1992}, Pages = {3--49}, Volume = {64}, DOI = {10.1103/RevModPhys.64.3} } @Article{MeWi94, author = {I. Mezi{\'c} and S. Wiggins}, title = {On the integrability and perturbation of three-dimensional fluid flows with symmetry}, journal = {J. Nonlin. Sci.}, year = {1994}, volume = {4}, pages = {157--194}, doi = {10.1007/bf02430631}, } @Book{Meyer00, title = {{Matrix Analysis and Applied Linear Algebra}}, publisher = {SIAM}, year = {2000}, author = {Meyer, C.}, isbn = {9780898714548}, address = {Philadelphia}, doi = {10.1137/1.9780898719512}, } @Article{Meyer86, author = {Meyer, K. R.}, title = {Counter-examples in dynamical systems via normal form theory}, journal = {SIAM Rev.}, year = {1986}, volume = {28}, pages = {41--51}, doi = {10.1137/1028002} } @Article{MFE04, author = {J. Moehlis and H. Faisst and B. Eckhardt}, title = {A low-dimensional model for turbulent shear flows}, journal = {New J. Phys.}, year = {2004}, volume = {6}, pages = {56}, doi = {10.1088/1367-2630/6/1/056}, } @Article{MFE04b, author = {J. Moehlis and H. Faisst and B. Eckhardt}, title = {Periodic orbits and chaotic sets in a low-dimensional model for shear flows}, journal = {SIAM J. Appl. Dyn. Syst.}, year = {2004}, volume = {4}, pages = {352--376}, doi = {10.1137/040606144}, } @Article{mfind, author = {Davidchack, R. L. and Lai, Y.-C.}, journal = {Phys. Rev. E}, title = {Efficient algorithm for detecting unstable periodic orbits in chaotic systems}, year = {1999}, pages = {6172}, volume = {60}, doi = {10.1103/physreve.60.6172}, } @Article{MFKM10, author = {Morita, Y. and Fujiwara, N. and Kobayashi, M. U. and Mizuguchi, T.}, title = {Scytale decodes chaos: {A} method for estimating unstable symmetric solutions}, journal = {Chaos}, year = {2010}, volume = {20}, pages = {013126}, doi = {10.1063/1.3365053}, } @Inproceedings{MH76, author = {Montroll, E. W. and Helleman, R. H. G.}, title = {On a nonlinear perturbation theory without secular terms {II. Carleman} embedding of nonlinear equations in an infinite set of linear ones}, booktitle = {{Topics in Statistical Mechanics and Biophysics: A Memorial to Julius L. Jackson}}, year = {1976}, volume = {27}, pages = {75--110}, doi = {10.1063/1.30362}, } @Book{MH94, title = {{Mathematical Foundations of Elasticity}}, publisher = {Dover}, year = {1994}, author = {Marsden, J. E. and Hughes, T. J. R.}, address = {New York}, isbn = {9780486678658}, doi = {10.1115/1.3167757}, } @Article{MHMwind96, author = {R. Montagne and E. Hern\'{a}ndez-Garc\'{i}a and M. S. Miguel}, title = {Winding number instability in the phase-turbulence regime of the complex {Ginzburg-Landau} equation}, journal = {Phys. Rev. Lett.}, year = {1996}, volume = {77}, pages = {267}, doi = {10.1103/physrevlett.77.267}, } @Article{michsiv77, author = {D. M. Michelson and G. I. Sivashinsky}, title = {Nonlinear analysis of hydrodynamic instability in laminar flames - {II}. Numerical experiments}, journal = {Acta Astronaut.}, year = {1977}, volume = {4}, pages = {1207--1221}, doi = {10.1016/0094-5765(77)90097-2}, } @Article{MicZhi01, author = {Michel, L. and Zhilinski{\'i}, B. I.}, journal = {Phys. Rep.}, title = {Symmetry, invariants, topology. {Basic} tools}, year = {2001}, pages = {11--84}, volume = {341}, doi = {10.1016/S0370-1573(00)00088-0}, } @Book{Mielke91, title = {{{Hamiltonian and Lagrangian} Flows on Center Manifolds}}, publisher = {Springer}, year = {1991}, author = {A. Mielke}, address = {New York}, doi = {10.1007/bfb0097544}, } @Book{Miller34, title = {{Tropic of Cancer}}, publisher = {Obelisk Press}, year = {1934}, author = {H. Miller}, address = {Paris}, url = {http://www.lib.ru/INPROZ/MILLER/tropikrakaengl.txt}, } @Article{milnor, Title = {Remarks on iterated cubic maps}, Author = {J. Milnor}, Journal = {Experiment. Math.}, Year = {1992}, Pages = {5--24}, Volume = {1}, DOI = {10.1080/10586458.1992.10504242} } @Misc{Milnor99, author = {Milnor, J. W.}, title = {Orbits, externals rays and the {Mandelbrot} set: {An} expository account}, year = {1999}, url = {https://arxiv.org/abs/math/9905169}, } @InCollection{MilThu88, author = {Milnor, J. and Thurston, W.}, booktitle = {{Dynamical Systems}}, publisher = {Springer}, title = {On iterated maps of the interval}, year = {1988}, address = {New York}, editor = {Alexander, J. C.}, pages = {465--563}, doi = {10.1007/BFb0082847}, } @TechReport{minpack, author = {Mor{\'e}, J. J. and Garbow, B. S. and Hillstrom, K. E.}, title = {{User Guide for MINPACK-1}}, institution = {Argonne National Lab.}, year = {1980}, type = {techreport}, number = {ANL-80-74}, url = {http://www.mcs.anl.gov/~more/ANL8074a.pdf}, } @Book{Mira87, title = {{{Chaotic Dynamics} - {From} One Dimensional Endomorphism to Two Dimen\-sional Diffeo\-morphism}}, publisher = {World Scientific}, year = {1987}, author = {C. Mira}, isbn = {978-9971-5-0324-6}, address = {Singapore}, } @Book{MiraGum80, title = {{Recurrances and Discrete Dynamical Systems}}, publisher = {Springer}, year = {1980}, author = {I. Gumowski and C. Mira}, address = {New York}, doi = {10.1007/bfb0089135}, } @Article{mis1, Title = {Strange attractors for the {Lozi} mapping}, Author = {Misiurewicz, M.}, Journal = {Ann. New York Acad. Sci.}, Year = {1980}, Pages = {348--358}, Volume = {357}, DOI = {10.1111/j.1749-6632.1980.tb29702.x} } @Article{misdis, author = {K. Mischaikow and M. Mrozek and J. Reiss and A. Szymczak}, title = {Construction of symbolic dynamics from experimental time series}, journal = {Phys. Rev. Lett.}, year = {1999}, volume = {82}, pages = {1144}, doi = {10.1103/physrevlett.82.1144}, } @Article{Misiurewicz81, Title = {Absolutely continuous measures for certain maps of an interval}, Author = {Misiurewicz, M.}, Journal = {Publ. Math. IHES}, Year = {1981}, Pages = {17--51}, Volume = {53}, URL = {http://www.numdam.org/item?id=PMIHES_1981__53__17_0} } @Article{mislor1, author = {K. Mischaikow and M. Mrozek}, title = {Chaos in the {Lorenz} equations: {A} computer assisted proof part {II}: {Details}}, journal = {Math. Comp.}, year = {1998}, volume = {67}, pages = {1023--1046}, doi = {10.1090/s0025-5718-98-00945-4}, } @Article{Misra96, author = {P. Misra}, journal = {Automatica}, title = {Time-invariant representation of discrete periodic systems}, year = {1996}, pages = {267--272}, volume = {32}, doi = {10.1016/0005-1098(96)85558-0}, } @Article{MIViana, author = {Viana, M.}, title = {What's new on {Lorenz} strange attractors?}, journal = {Math. Intelligencer}, year = {2000}, volume = {22}, pages = {6--19}, doi = {10.1007/bf03025276}, } @Article{MiZg01, author = {M. Misiurewicz and P. Zgliczynski}, title = {Topological entropy for multidimensional perturbations of one dimensional maps}, journal = {Int. J. Bifur. Chaos}, year = {2001}, volume = {5}, pages = {1443--1446}, doi = {10.1142/s021812740100281x}, } @Article{MKMP84, Title = {Transport in {Hamiltonian} systems}, Author = {R. S. MacKay and J. D. Meiss and I. C. Percival}, Journal = {Physica D}, Year = {1984}, Pages = {55--81}, Volume = {13}, DOI = {10.1016/0167-2789(84)90270-7} } @Article{Mkrtchyan16, author = {Mkrtchyan, R. L.}, title = {On the road map of {Vogel's} plane}, journal = {Lett. Math. Phys.}, year = {2016}, volume = {106}, pages = {57--79}, doi = {10.1007/s11005-015-0803-9}, } @Article{Mks86, Title = {Steady solutions of the {Kuramoto-Sivashinsky} equation}, Author = {D. Michelson}, Journal = {Physica D}, Year = {1986}, Pages = {89--111}, Volume = {19}, DOI = {10.1016/0167-2789(86)90055-2} } @Article{MoeJosPO, author = {J. Moehlis and K. Josi{\'c} and E. T. Shea-Brown}, title = {Periodic orbit}, journal = {Scholarpedia}, year = {2006}, volume = {1}, pages = {1358}, doi = {10.4249/scholarpedia.1358}, } @Misc{Molteni16, Title = {An efficient method for the computation of the {Feigenbaum} constants to high precision}, Author = {Molteni, A.}, Year = {2016}, URL = {https://arXiv.org/abs/1602.02357} } @Book{Moon87, title = {{Chaotic Vibrations: An Introduction for Applied Scientists and Engineers}}, publisher = {Wiley}, year = {1987}, author = {F. C. Moon}, isbn = {978-0-471-67908-0}, address = {New York}, doi = {10.1002/3527602844}, } @Article{Mor06, author = {K. W. Morton}, journal = {SIAM Rev.}, title = {Book review: simulating {Hamiltonian} dynamics}, year = {2006}, pages = {621--623}, volume = {48}, doi = {10.1090/s0025-5718-05-01877-6}, } @PhdThesis{Morena14, author = {Morena, M. A.}, school = {Univ. New Hampshire}, title = {{Mutual stabilization of chaotic systems through entangled cupolets}}, year = {2014}, adsurl = {http://adsabs.harvard.edu/abs/2014PhDT........89M}, doi = {9781321102468}, } @Inproceedings{Morkovin69, author = {M. V. Morkovin}, title = {On the many faces of transition}, booktitle = {Viscous Drag Reduction}, year = {1969}, editor = {C. S. Wells}, pages = {1--31}, address = {New York}, publisher = {Plenum}, doi = {10.1007/978-1-4899-5579-1_1}, } @Article{Moran46, author = {P. A. P. Moran}, journal = {Proc. Camb. Phil. Soc.}, title = {Additive functions of intervals and {Hausdorff} measure}, year = {1946}, pages = {15}, volume = {42}, doi = {10.1017/S0305004100022684}, } @Article{Morr80, author = {Morrison, P. J.}, title = {The {Maxwell-Vlasov} equations as a continuous {Hamiltonian} system}, journal = {Phys. Lett. A}, year = {1980}, volume = {80}, pages = {383--386}, doi = {10.2172/5017455}, } @Article{Morr98, author = {Morrison, P. J.}, title = {Hamiltonian description of the ideal fluid}, journal = {Rev. Mod. Phys.}, year = {1998}, volume = {70}, pages = {467--521}, doi = {10.2172/10128748}, } @Article{MorrGree80, author = {Morrison, P. J. and Greene, J. M.}, journal = {Phys. Rev. Lett.}, title = {Noncanonical {Hamiltonian} density formulation of hydrodynamics and ideal magnetohydrodynamics}, year = {1980}, note = {See also Phys. Rev. Lett. 48, 569 (1982)}, pages = {790--794}, volume = {45}, doi = {10.1103/PhysRevLett.45.790}, } @Article{Morrison02, author = {J. F. Morrison and W. Jiang and B. J. McKeon and A. J. Smits}, title = {Reynolds number dependence of streamwise velocity spectra in turbulent pipe flow}, journal = {Phys. Rev. Lett.}, year = {2002}, volume = {88}, pages = {214501}, doi = {10.1103/physrevlett.88.214501}, } @Article{Morrison04, author = {J. F. Morrison and B. J. McKeon and W. Jiang and A. J. Smits}, title = {Scaling of the streamwise velocity component in turbulent pipe flow}, journal = {J. Fluid Mech.}, year = {2004}, volume = {508}, pages = {99--131}, doi = {10.1017/s0022112004008985}, } @Misc{MorSho13, Title = {Cupolets and a chaotic analog of entanglement}, Author = {Morena, M. and Short, K.}, Year = {2013}, URL = {https://arXiv.org/abs/1302.2283} } @Article{MorSho14, Title = {On the potential for entangled states between chaotic systems}, Author = {Morena, M. and Short, K.}, Journal = {Int. J. Bifur. Chaos}, Year = {2014}, Pages = {1450077}, Volume = {24}, DOI = {10.1142/S0218127414500771} } @Article{Moser94, author = {J. K. Moser}, title = {On quadratic symplectic mappings}, journal = {Math. Z.}, year = {1994}, volume = {216}, pages = {417--430}, doi = {10.1007/BF02572331} } @Book{mosersr, title = {{Stable and Random Motions in Dynamical Systems}}, publisher = {Princeton Univ. Press}, year = {1973}, author = {J. Moser}, series = {Ann. Math. Stud.}, address = {Princeton}, } @Article{MoShCo14, Title = {Controlled transitions between cupolets of chaotic systems}, Author = {Morena, M. A. and Short, K. M. and Cooke, E. E.}, Journal = {Chaos}, Year = {2014}, Pages = {013111}, Volume = {24}, DOI = {10.1063/1.4862668} } @Article{Moss94, Title = {Chaos under control}, Author = {F. Moss}, Journal = {Nature}, Year = {1994}, Pages = {596--597}, Volume = {370}, DOI = {10.1038/370596a0} } @Article{Mostow57, Title = {Equivariant embeddings in {Euclidean} space}, Author = {G. D. Mostow}, Journal = {Ann. Math.}, Year = {1957}, Pages = {432--446}, Volume = {65}, DOI = {10.2307/1970055} } @Article{Motter09, author = {Motter, Adilson E. and Gelfert, Katrin}, title = {Time-metric equivalence and dimension change under time reparameterizations}, journal = {Phys. Rev. E}, year = {2009}, volume = {79}, pages = {065202}, doi = {10.1103/physreve.79.065202}, } @Article{MP79, Title = {Intermittency and the {Lorenz} model}, Author = {Manneville, P. and Pomeau, Y.}, Journal = {Phys. Lett. A}, Year = {1979}, Pages = {1--2}, Volume = {75}, DOI = {10.1016/0375-9601(79)90255-X} } @Article{MR88, Title = {Stochastic modeling of a billiard in a gravitational field: {Power} law behavior of {Lyapunov} exponents}, Author = {B. N. Miller and K. Ravishankar}, Journal = {J. Stat. Phys.}, Year = {1988}, Pages = {1299}, Volume = {53}, DOI = {10.1007/BF01023870} } @Article{MR96, Title = {Stationary nonequilibrium ensembles for thermostated systems}, Author = {L. Rondoni and G. P. Morriss}, Journal = {Phys. Rev. E}, Year = {1996}, Pages = {2143}, Volume = {53}, DOI = {10.1103/PhysRevE.53.2143} } @Article{MR97, Title = {Applications of periodic orbit theory to {N}-particle systems}, Author = {L. Rondoni and G. P. Morriss}, Journal = {J. Stat. Phys.}, Year = {1997}, Pages = {991--1009}, Volume = {86}, DOI = {10.1007/BF02183611} } @Article{MRC94, Title = {A dynamical partition function for the {Lorentz} gas}, Author = {G. P. Morriss and L. Rondoni and E. G. D. Cohen}, Journal = {J. Stat. Phys.}, Year = {1995}, Pages = {35--43}, Volume = {80}, DOI = {10.1007/BF02178352} } @Article{MRTK07, author = {Marwan, N. and Romano, M. C. and Thiel, M. and Kurths, J.}, title = {Recurrence plots for the analysis of complex systems}, journal = {Phys. Rep.}, year = {2007}, volume = {438}, pages = {237}, doi = {10.1016/j.physrep.2006.11.001}, } @Article{MS66, author = {D. W. Moore and E. A. Spiegel}, title = {A thermally excited nonlinear oscillator}, journal = {Astrophys. J.}, year = {1966}, volume = {143}, pages = {871--887}, doi = {10.1086/148562}, } @Article{MSS73, author = {N. Metropolis and M. L. Stein and P. R. Stein}, title = {On finite limit sets for transformations on the unit interval}, journal = {J. Combin. Theory}, year = {1973}, volume = {15}, pages = {25--44}, doi = {10.1016/0097-3165(73)90033-2}, } @Article{MSuzuki91, author = {M. Suzuki}, title = {General theory of fractal path integrals with applications to many-body theories and statistical physics}, journal = {J. Math. Phys.}, year = {1991}, volume = {32}, pages = {400}, doi = {10.1063/1.529425}, } @Book{mta, author = {R. Abraham and J. E. Marsden and T. S. Ratiu}, publisher = {Springer}, title = {{Manifolds, Tensor Analysis, and Applications}}, year = {1988}, address = {New York}, edition = {2}, isbn = {978-1-4612-1029-0}, doi = {10.1007/978-1-4612-1029-0}, } @Article{muloz-almaraz_continuation_2007, author = {{Mu{\~n}oz-Almaraz}, F. J. and Freire, E. and Galan, J. and Vanderbauwhede, A.}, journal = {Celestial Mech. Dynam. Astronom.}, title = {Continuation of normal doubly symmetric orbits in conservative reversible systems}, year = {2007}, pages = {17--47}, volume = {97}, doi = {10.1007/s10569-006-9048-3}, } @Article{munoz-almaraz_continuation_2003, author = {Mu{\~n}oz-Almaraz, F. J. and Freire, E. and Galan, J. and Doedel, E. J. and Vanderbauwhede, A.}, title = {Continuation of periodic orbits in conservative and {Hamiltonian} systems}, journal = {Physica D}, year = {2003}, volume = {181}, pages = {1--38}, doi = {10.1016/s0167-2789(03)00097-6}, } @Article{Murat03, author = {Muratore-Ginanneschi, P.}, title = {Path integration over closed loops and {Gutzwiller}'s trace formula}, journal = {Phys. Rep.}, year = {2002}, volume = {383}, pages = {299--397}, doi = {10.1016/S0370-1573(03)00212-6}, } @Article{MvH98, author = {M. van Hecke}, title = {Building blocks of spatiotemporal intermittency}, journal = {Phys. Rev. Lett.}, year = {1998}, volume = {80}, pages = {1896}, doi = {10.1103/physrevlett.80.1896}, } @Article{MvHhole01, author = {M. van Hecke and M. Howard}, title = {Ordered and self-disordered dynamics of holes and defects in the one-dimensional complex {Ginzburg-Landau} equation}, journal = {Phys. Rev. Lett.}, year = {2001}, volume = {86}, pages = {2018}, doi = {10.1103/physrevlett.86.2018}, } @Misc{mwResultant, author = {Weisstein, E. W.}, title = {Resultant of two polynomials}, year = {2016}, publisher = {Wolfram MathWorld}, url = {http://mathworld.wolfram.com/Resultant.html}, } @Article{Myrberg58a, author = {Myrberg, P. J.}, journal = {Ann. Acad. Sc. Fenn. A}, title = {{Iteration der reellen Polynome zweiten Grades I}}, year = {1958}, pages = {1--10}, volume = {256}, url = {http://inaesp.org/Legacy/myrberg_256_1958.pdf}, } @Article{Myrberg58b, author = {Myrberg, P. J.}, title = {Iteration von quadratwurzeloperationen}, journal = {Ann. Acad. Sc. Fenn. A}, year = {1958}, volume = {259}, pages = {1--10}, url = {http://inaesp.org/Legacy/myrberg_259_1958.pdf} } @Article{Myrberg59, author = {Myrberg, P. J.}, journal = {Ann. Acad. Sc. Fenn. A}, title = {{Iteration der reellen Polynome zweiten Grades II}}, year = {1959}, pages = {1--13}, volume = {268}, url = {http://inaesp.org/Legacy/myrberg_iteration_polynome_teil2_268_1959.pdf}, } @Article{Myrberg62, author = {Myrberg, P. J.}, title = {Sur l'it{\'e}ration des polynomes r{\'e}els quadratiques}, journal = {J. Math. Pures Appl.}, year = {1962}, volume = {41}, pages = {339--351}, url = {http://inaesp.org/Legacy/myrberg_polynomes_quadratiques_JMPA1962.pdf} } @Article{Myrberg63, author = {Myrberg, P. J.}, journal = {Ann. Acad. Sc. Fenn. A}, title = {{Iteration der reellen Polynome zweiten Grades III}}, year = {1963}, pages = {1--13}, volume = {336}, url = {http://inaesp.org/Legacy/myrberg_336_1963.pdf}, } @Article{myrh1, Title = {Universality for period n-tuplings in complex mappings}, Author = {Cvitanovi{\'c}, P. and Myrheim, J.}, Journal = {Phys. Lett. A}, Year = {1983}, Pages = {329--333}, Volume = {94}, DOI = {10.1016/0375-9601(83)90121-4} } @Article{N90, Title = {Three-dimensional finite-amplitude solutions in plane {Couette} flow: bifurcation from infinity.}, Author = {M. Nagata}, Journal = {J. Fluid Mech.}, Year = {1990}, Pages = {519--527}, Volume = {217}, DOI = {10.1017/S0022112090000829} } @Book{Naka90, title = {{Geometry, Topology and Physics}}, publisher = {Inst. of Physics Publ.}, year = {1990}, author = {M. Nakahara}, isbn = {9780750306065}, address = {Bristol}, doi = {10.1887/0750306068}, } @Article{NaSVa14, author = {N{\'a}ndori, P. and Sz{\'a}sz, D. and Varj{\'u}, T.}, journal = {Commun. Math. Phys.}, title = {Tail asymptotics of free path lengths for the periodic {Lorentz} process: on {Dettmann}'s geometric conjectures}, year = {2014}, pages = {111--137}, volume = {331}, doi = {10.1007/s00220-014-2086-x}, } @Book{nelson85, Title = {{Quantum Fluctuations}}, Author = {Nelson, E.}, Publisher = {Princeton Univ. Press}, Year = {1985}, URL = {https://web.math.princeton.edu/~nelson/books/qf.pdf} } @Article{neumann, author = {J. von Neumann and E. P. Wigner}, title = {{Uber merkw{\"u}rdige diskrete Eigenwerte. Uber das Verhalten von Eigenwerten bei adiabatischen Prozessen}}, journal = {Phys. Zeit.}, year = {1929}, volume = {30}, pages = {467--470}, } @Article{newcgl1, author = {P. K. {Newton} and L. Sirovich}, title = {Instabilities of {Ginzburg-Landau} equation: periodic solutions}, journal = {Quart. Appl. Math.}, year = {1986}, volume = {44}, pages = {49--58}, doi = {10.1090/qam/840442}, } @Article{newcgl2, author = {P. K. {Newton} and L. Sirovich}, title = {Instabilities of {Ginzburg-Landau} equation: secondary bifurcation}, journal = {Quart. Appl. Math.}, year = {1986}, volume = {44}, pages = {367--374}, doi = {10.1090/qam/856192}, } @Article{newenv74, Title = {Envelope equations}, Author = {A. C. Newell}, Journal = {Lect. Appl. Math.}, Year = {1974}, Pages = {157--163}, Volume = {15} } @Article{nhouse74, author = {Newhouse, S. E.}, title = {Diffeomorphisms with infinitely many sinks}, journal = {Topology}, year = {1974}, volume = {13}, pages = {9--18}, doi = {10.1016/0040-9383(74)90034-2}, } @Article{nhouse78, author = {S. E. Newhouse and D. Ruelle and F. Takens}, title = {Occurrence of strange {Axiom A} attractors near quasi-periodic flows on {${T}^m$} ({$m=3$} or more)}, journal = {Commun. Math. Phys.}, year = {1978}, volume = {64}, pages = {35--40}, doi = {10.1007/BF01940759}, } @Article{nhouse79, author = {Newhouse, S. E.}, title = {The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms}, journal = {Publ. Math. IHES}, year = {1979}, volume = {50}, pages = {101--152}, doi = {10.1007/BF02684771}, } @Article{NicKim16, Title = {Geometric method for forming periodic orbits in the {Lorenz} system}, Author = {Nicholson, S. B. and Kim, E.-J.}, Journal = {Physica Scripta}, Year = {2016}, Pages = {044006}, Volume = {91}, DOI = {10.1088/0031-8949/91/4/044006} } @Article{NiDaCv99, Title = {Periodic orbit sum rules for billiards: {Accelerating} cycle expansions}, Author = {Nielsen, S. F. and Dahlqvist, P. and Cvitanovi{\'c}, P.}, Journal = {J. Phys. A}, Year = {1999}, Pages = {6757--6770}, Volume = {32}, DOI = {10.1088/0305-4470/32/39/304} } @Article{NiHa91, Title = {Phase anholonomy in dissipative optical-systems with periodic oscillations}, Author = {Ning, C. Z. and Haken, H.}, Journal = {Phys. Rev. A}, Year = {1991}, Pages = {6410--6413}, Volume = {43}, DOI = {10.1103/PhysRevA.43.6410} } @Article{NiHa92, Title = {An invariance property of the geometrical phase and its consequence in detuned lasers}, Author = {Ning, C. Z. and Haken, H.}, Journal = {Z. Phys. B}, Year = {1992}, Pages = {261--262}, Volume = {89}, DOI = {10.1007/BF01318153} } @Article{NiHa92a, Title = {Geometrical phase and amplitude accumulations in dissipative systems with cyclic attractors}, Author = {C. Z. Ning and H. Haken}, Journal = {Phys. Rev. Lett.}, Year = {1992}, Pages = {2109--2112}, Volume = {68}, DOI = {10.1103/PhysRevLett.68.2109} } @Article{NingHakenCLE90, author = {Ning, C. Z. and Haken, H.}, title = {Detuned lasers and the complex {Lorenz} equations: {Subcritical} and supercritical {H}opf bifurcations}, journal = {Phys. Rev.}, year = {1990}, volume = {41}, pages = {3826}, doi = {10.1103/physreva.41.3826}, } @Article{NLSmal91, author = {B. A. Malomed and L. Stenflo}, title = {Modulational instabilities and soliton solutions of a generalized nonlinear {Schr{\"{o}}dinger} equation}, journal = {J. Phys. A}, year = {1991}, volume = {24}, pages = {L1149--L1153}, doi = {10.1088/0305-4470/24/19/006}, } @Article{NLSper77, author = {N. R. Pereira and L. Stenflo}, title = {Nonlinear {Schr{\"{o}}dinger} equation including growth and damping}, journal = {Phys. Fluid}, year = {1977}, volume = {20}, pages = {1733--1734}, doi = {10.1063/1.861773}, } @Article{NLSstn03, author = {L. Stenflo and M. Y. Yu}, title = {Oscillons at a plasma surface}, journal = {Phys. Plasmas}, year = {2003}, volume = {10}, pages = {912--913}, doi = {10.1063/1.1555625}, } @Article{Noether15, Title = {{Der Endlichkeitssatz der Invarianten endlicher Gruppen}}, Author = {Noether, E.}, Journal = {Math. Ann.}, Year = {1915}, Pages = {89--92}, Volume = {77}, DOI = {10.1007/BF01456821} } @Article{Noether18, author = {Noether, E.}, title = {{Invariante Variationsprobleme}}, journal = {Nachr. Ges. Wiss. Gottingen, Math.-Phys.}, year = {1918}, volume = {1918}, pages = {235--257}, url = {http://eudml.org/doc/59024}, } @Article{noisy_Fred, author = {Cvitanovi{\'c}, P. and Dettmann, C. P. and Mainieri, R. and Vattay, G.}, title = {Trace formulas for stochastic evolution operators: {Weak} noise perturbation theory}, journal = {J. Stat. Phys.}, year = {1998}, volume = {93}, pages = {981--999}, doi = {10.1023/B:JOSS.0000033173.38345.f9}, } @Book{Nomizu79, title = {{Fundamentals of Linear Algebra}}, publisher = {Chelsea Publ.}, year = {1979}, author = {K. Nomizu}, isbn = {9780828402767}, address = {New York}, } @Article{nongal89, author = {M. Martine and R. T{\'e}mam}, title = {Nonlinear {G\"{a}lerkin} methods}, journal = {SIAM J. Numer. Anal.}, year = {1989}, volume = {26}, pages = {1139--1157}, doi = {10.1137/0726063}, } @Article{Nonnen03, author = {S. Nonnenmacher}, title = {Spectral properties of noisy classical and quantum propagators}, journal = {Nonlinearity}, year = {2003}, volume = {16}, pages = {1685--1713}, doi = {10.1088/0951-7715/16/5/309} } @Article{Nordahl1989, Title = {Formal languages and finite cellular automata}, Author = {Nordahl, M.}, Journal = {Complex Systems}, Year = {1989}, Pages = {6--78}, Volume = {3}, URL = {http://www.complex-systems.com/abstracts/v03_i01_a05.html} } @Article{NP, author = {K. Lust and D. Roose}, title = {An adaptive {Newton-Picard} algorithm with subspace iteration for computing periodic solutions}, journal = {SIAM J. Sci. Comput.}, year = {1998}, volume = {19}, pages = {1188--1209}, doi = {10.1137/s1064827594277673}, } @Article{npcs, Title = {Complex generalization of approximate renormalization group analysis and {Mandelbrot} set. {Thermodynamic} analogy}, Author = {O. B. Isaeva and S. P. Kuznetsov}, Journal = {Nonlin. Phen. Compl. Syst.}, Year = {2005}, Pages = {157--165}, Volume = {8}, URL = {http://www.j-npcs.org/online/vol2005/v8no2/v8no2p157.pdf} } @Book{nr, author = {W. H. Press and S. A. Teukolsky and W. T. Vetterling and B. P. Flannery}, publisher = {Cambridge Univ. Press}, title = {{Numerical Recipes in {C}}}, year = {1992}, address = {Cambridge UK}, } @Book{ns, title = {{Numerical Partial Differential Equations}}, publisher = {Springer}, year = {1995}, author = {J. W. Thomas}, address = {New York}, doi = {10.1007/978-1-4612-0569-2}, } @Article{NSTks85, author = {B. Nicolaenko and B. Scheurer and R. T{\'e}mam}, title = {Some global dynamical properties of the {Kuramoto-Sivashinsky} equations: nonlinear stability and attractors}, journal = {Physica D}, year = {1985}, volume = {16}, pages = {155--183}, doi = {10.1016/0167-2789(85)90056-9}, } @Book{NussYo97, title = {{Dynamics: Numerical Explorations}}, publisher = {Springer}, year = {1997}, author = {H. E. Nusse and J. A. Yorke}, isbn = {978-0-387-98264-9}, address = {New York}, doi = {10.1007/978-1-4684-0231-5}, } @Article{OG97, Title = {Bifurcations and chaos for the quasiperiodic bouncing ball}, Author = {C. R. de Oliveira and P. S. Gon{\c{c}}alves}, Journal = {Phys. Rev. E}, Year = {1997}, Pages = {4868--4871}, Volume = {56}, DOI = {10.1103/PhysRevE.56.4868} } @Article{OGY89, Title = {Theory of first order phase transitions for chaotic attractors of nonlinear dynamical systems}, Author = {Ott, E. and Grebogi, C. and Yorke, J. A.}, Journal = {Phys. Lett. A}, Year = {1989}, Pages = {343--348}, Volume = {135}, DOI = {10.1016/0375-9601(89)90005-4} } @Book{Oksendal03, author = {{\O}ksendal, B. K.}, publisher = {Springer}, title = {{Stochastic Differential Equations: An Introduction with Applications}}, year = {1998}, address = {New York}, isbn = {9783540637202}, } @Article{Okubo62, Title = {Note on unitary symmetry in strong interactions}, Author = {Okubo, S.}, Journal = {Progr. Theor. Phys.}, Year = {1962}, Pages = {949--966}, Volume = {27}, DOI = {10.1143/PTP.27.949} } @Article{OlGo92, Title = {Isotropic-nematic transition in shear flow: {State} selection, coexistence, phase transitions, and critical behavior}, Author = {Olmsted, P. D. and Goldbart, P. M.}, Journal = {Phys. Rev. A}, Year = {1992}, Pages = {4966--4993}, Volume = {46}, DOI = {10.1103/PhysRevA.46.4966} } @Article{OlLe11, author = {Oliveira, D. F. M. and Leonel, E. D.}, journal = {Brazilian J. Physics}, title = {The {Feigenbaum}'s {$\delta$} for a high dissipative bouncing ball model}, year = {2011}, pages = {62--64}, volume = {38}, eprint = {1101.4596}, eprinttype = {arxiv}, } @Article{Olmsted94, Title = {Rotational invariance and {Goldstone modes} in nematic elastomers and gels}, Author = {Olmsted, P. D.}, Journal = {J. Phys. II France}, Year = {1994}, Pages = {2215--2230}, Volume = {4}, DOI = {10.1051/jp2:1994257} } @Book{Olver09, author = {P. J. Olver}, publisher = {Cambridge Univ. Press}, title = {{Equivalence, Invariants and Symmetry}}, year = {2009}, address = {Cambridge UK}, isbn = {9780521101042}, } @Book{Olver14, title = {{Introduction to Partial Differential Equations}}, publisher = {Springer}, year = {2014}, author = {P. J. Olver}, isbn = {978-3-319-02098-3}, address = {New York}, doi = {10.1007/978-3-319-02099-0}, } @Book{OlverInv, author = {P. J. Olver}, publisher = {Cambridge Univ. Press}, title = {{Classical Invariant Theory}}, year = {1999}, address = {Cambridge UK}, doi = {10.1017/cbo9780511623660}, } @Article{Onsager31I, Title = {Reciprocal relations in irreversible processes. {I.}}, Author = {Onsager, L.}, Journal = {Phys. Rev.}, Year = {1931}, Pages = {405--426}, Volume = {37}, DOI = {10.1103/PhysRev.37.405} } @Article{Onsager31II, Title = {Reciprocal relations in irreversible processes. {II.}}, Author = {Onsager, L.}, Journal = {Phys. Rev.}, Year = {1931}, Pages = {2265--2279}, Volume = {38}, DOI = {10.1103/PhysRev.38.2265} } @Article{Onsager53, Title = {Fluctuations and irreversible processes}, Author = {L. Onsager and S. Machlup}, Journal = {Phys. Rev.}, Year = {1953}, Pages = {1505--1512}, Volume = {91}, DOI = {10.1103/PhysRev.91.1505} } @Article{Onsager53II, Title = {Fluctuations and irreversible processes. {II. Systems} with kinetic energy}, Author = {Machlup, S. and Onsager, L.}, Journal = {Phys. Rev.}, Year = {1953}, Pages = {1512--1515}, Volume = {91}, DOI = {10.1103/PhysRev.91.1512} } @Article{optp1, author = {B. R. Hunt and E. Ott}, title = {Optimal periodic orbits of chaotic systems}, journal = {Phys. Rev. Lett.}, year = {1996}, volume = {76}, pages = {2254}, doi = {10.1103/physrevlett.76.2254}, } @Article{optp2, author = {T.-H. Yang and B. R. Hunt and E. Ott}, title = {Optimal periodic orbits of continuous time chaotic systems}, journal = {Phys. Rev. E}, year = {2000}, volume = {62}, pages = {1950}, doi = {10.1103/physreve.62.1950}, } @Techreport{orbit, Title = {On locating homoclinic and heteroclinic orbits}, Author = {Doedel, E. J. and Friedman, M. J. and Monteiro, A. C.}, Institution = {Center for Applied Mathematics, Cornell Univ.}, Year = {1993} } @Article{Ordonez96, author = {G. E. Ordonez and D. J. Driebe}, title = {Spectral decomposition of tent maps using symmetry considerations}, journal = {J. Stat. Phys.}, year = {1996}, volume = {84}, pages = {269--276}, doi = {10.1007/BF02179586}, } @Article{OrnUhl30, Title = {On the theory of the {Brownian} motion}, Author = {Uhlenbeck, G. E. and Ornstein, L. S.}, Journal = {Phys. Rev.}, Year = {1930}, Pages = {823--841}, Volume = {36}, DOI = {10.1103/PhysRev.36.823} } @Article{Orr1907, Title = {The stability or instability of the steady motions of a liquid. {Part II: A} viscous liquid}, Author = {Orr, W. M. F.}, Journal = {Proc. R. Irish. Acad. A}, Year = {1907}, Pages = {69--138}, Volume = {27}, URL = {http://profs.princeton.edu/leo/journals/Orr-CouetteFlowInstabViscous-ProcRoyIrAcaSci-1909.pdf} } @Article{Orsucci2006, author = {Orsucci, F. F.}, title = {The paradigm of complexity in clinical neurocognitive science}, journal = {The Neuroscientist}, year = {2006}, volume = {12}, pages = {390--397}, doi = {10.1177/1073858406290266}, publisher = {SAGE Publications}, } @Article{Orszag1, author = {S. A. Orszag and M. Israeli and M. Deville}, title = {Boundary conditions for incompressible flows}, journal = {J. Sci. Comput.}, year = {1986}, volume = {1}, pages = {75--111}, doi = {10.1007/bf01061454}, } @Article{Orszag71, author = {S. A. Orszag}, title = {Accurate solution of the {Orr-Sommerfeld} stability equation}, journal = {J. Fluid Mech.}, year = {1971}, volume = {50}, pages = {689--703}, doi = {10.1017/s0022112071002842}, } @Article{OT80, author = {Y. Oono and Y. Takahashi}, title = {Chaos, external noise and {Fredholm} theory}, journal = {Progr. Theor. Phys.}, year = {1980}, volume = {63}, pages = {1804--1807}, doi = {10.1143/PTP.63.1804} } @Book{ott, author = {E. Ott}, publisher = {Cambridge Univ. Press}, title = {{Chaos and Dynamical Systems}}, year = {2002}, address = {Cambridge UK}, doi = {10.1017/cbo9780511803260}, } @Article{Ott1990, Title = {Controlling chaos}, Author = {E. Ott and C. Grebogi and J. A. Yorke}, Journal = {Phys. Rev. Lett.}, Year = {1990}, Pages = {1196--1199}, Volume = {64}, DOI = {10.1103/PhysRevLett.64.1196} } @Article{OzoHan84, author = {Ozorio de Almeida, A. M. and Hannay, J. H.}, title = {Periodic orbits and a correlation function for the semiclassical density of states}, journal = {J. Phys. A}, year = {1984}, volume = {17}, pages = {3429}, doi = {10.1088/0305-4470/17/18/013}, } @Article{Ozorio, author = {Ozorio de Almeida, A. M. and Hannay, J. H.}, title = {Resonant periodic orbits and the semiclassical energy spectrum}, journal = {J. Phys. A}, year = {1987}, volume = {20}, pages = {5873}, doi = {10.1088/0305-4470/20/17/021}, } @Article{PaCrFaSh80, author = {Packard, N. H. and Crutchfield, J. P. and Farmer, J. D. and Shaw, R. S.}, journal = {Phys. Rev. Lett.}, title = {Geometry from a time series}, year = {1980}, pages = {712--716}, volume = {45}, doi = {10.1103/physrevlett.45.712}, } @Article{PaiL81, Title = {A {Schur} decomposition for {Hamiltonian} matrices}, Author = {Paige, C. C. and Van Loan, C.}, Journal = {Linear Algebra Appl.}, Year = {1981}, Pages = {11--32}, Volume = {41}, DOI = {10.1016/0024-3795(81)90086-0} } @Article{Pal61, Title = {On the existence of slices for actions of non-compact {Lie} groups}, Author = {R. S. Palais}, Journal = {Ann. Math.}, Year = {1961}, Pages = {295--323}, Volume = {73}, URL = {http://www.jstor.org/stable/1970335} } @Article{PaLo10, author = {Paz{\'o}, D. and L{\'o}pez, J. M.}, title = {Characteristic {Lyapunov} vectors in chaotic time-delayed systems}, journal = {Phys. Rev. E}, year = {2010}, volume = {82}, pages = {056201}, doi = {10.1103/physreve.82.056201}, } @Article{PaLuSr00, author = {Pance, K. and Lu, W. and Sridhar, S.}, journal = {Phys. Rev. Lett.}, title = {Quantum fingerprints of classical {Ruelle-Pollicott} resonances}, year = {2000}, pages = {2737--2740}, volume = {85}, doi = {10.1103/PhysRevLett.85.2737}, } @Article{Parry86, Title = {Synchronisation of canonical measures for hyperbolic attractors}, Author = {W. Parry}, Journal = {Commun. Math. Phys.}, Year = {1986}, Pages = {267--275}, Volume = {106}, DOI = {10.1007/BF01454975} } @Article{ParSour82, author = {G. Parisi and N. Sourlas}, journal = {Nucl. Phys. B}, title = {Supersymmetric field theories and stochastic differential equations}, year = {1982}, pages = {321--332}, volume = {206}, doi = {10.1016/0550-3213(82)90538-7}, } @Article{paskauskas09, author = {R. Pa\v{s}kauskas and G. {De Ninno}}, title = {{Lyapunov} stability of {Vlasov} equilibria using {Fourier-{Hermit}e} modes}, journal = {Phys. Rev. E}, year = {2009}, volume = {80}, pages = {036402}, doi = {10.1103/physreve.80.036402}, } @Article{PaSzLoRo09, author = {D. Paz{\'o} and I. G. Szendro and J. M. L{\'o}pez and M. A. Rodr{\'i}guez}, title = {Structure of characteristic {Lyapunov} vectors in spatiotemporal chaos}, journal = {Phys. Rev. E}, year = {2008}, volume = {78}, pages = {016209}, doi = {10.1103/physreve.78.016209}, } @Article{PCar, Title = {Group theory for {Feynman} diagrams in non-{Abelian} gauge theories}, Author = {Cvitanovi{\'c}, P.}, Journal = {Phys. Rev. D}, Year = {1976}, Pages = {1536--1553}, Volume = {14}, DOI = {10.1103/PhysRevD.14.1536} } @Inbook{PCgrIntegr, chapter = {Group Integrals}, title = {{Group Theory} - {Birdtracks}, {Lie}'s, and {Exceptional Groups}}, publisher = {Princeton Univ. Press}, year = {2008}, author = {P. Cvitanovi{\'c}}, address = {Princeton, NJ}, doi = {10.1515/9781400837670}, url = {http://birdtracks.eu}, } @Article{pchaot, Title = {Exploring chaotic motion through periodic orbits}, Author = {D. Auerbach and P. Cvitanovi{\'c} and J.-P. Eckmann and G. Gunaratne and I. Procaccia}, Journal = {Phys. Rev. Lett.}, Year = {1987}, Pages = {2387--2389}, Volume = {58}, DOI = {10.1103/PhysRevLett.58.2387} } @Article{PDescape, Title = {Escape from intermittent repellers: {Periodic} orbit theory for crossover from exponential to algebraic decay}, Author = {Dahlqvist, P.}, Journal = {Phys. Rev. E}, Year = {1999}, Pages = {6639--6644}, Volume = {60}, DOI = {10.1103/PhysRevE.60.6639} } @Article{PDprun97, Title = {On the effect of pruning on the singularity structure of zeta functions}, Author = {Dahlqvist, P.}, Journal = {J. Math. Phys.}, Year = {1997}, Pages = {4273--4282}, Volume = {38}, DOI = {10.1063/1.532094} } @Article{PDresum, Title = {Computing the topological pressure for intermittent maps}, Author = {Dahlqvist, P.}, Journal = {J. Phys. A}, Year = {1997}, Pages = {L351--L358}, Volume = {30}, DOI = {10.1088/0305-4470/30/11/002} } @Article{Peckham_1998, author = {B. Peckham}, title = {Real perturbation of complex analitic families: {Points} to regions}, journal = {Int. J. Bifur. Chaos}, year = {1998}, volume = {8}, pages = {73--93}, doi = {10.1142/s0218127498000061}, } @Article{Peinke, Title = {Instability of the {Mandelbrot} set}, Author = {J. Peinke and J. Parisi, B. R{\"o}hricht and O. E. R{\"o}ssler}, Journal = {Z. Naturf. A}, Year = {1987}, Pages = {263}, Volume = {42}, DOI = {10.1515/zna-1987-0309} } @Book{Peitgen, title = {{The Beauty of Fractals. Images of Complex Dynamical Systems}}, publisher = {Springer}, year = {1986}, author = {H. O. Peitgen and P. H. Richter}, address = {Berlin}, doi = {10.2307/1578666}, } @Book{PeJuSa04, title = {{Chaos and Fractals: New Frontiers of Science}}, publisher = {Springer}, year = {2004}, author = {Peitgen, H.-O. and J{\"u}rgens, H. and Saupe, D.}, isbn = {978-1-4684-9396-2}, address = {New York}, doi = {10.2307/3620111}, } @Book{Penr04, author = {R. Penrose}, publisher = {A. A. Knopf}, title = {{The Road to Reality} - {A Complete Guide to the Laws of the Universe}}, year = {2005}, address = {New York}, isbn = {9781446418208}, } @InCollection{Penrose1971, author = {Penrose, R.}, booktitle = {{Combinatorial mathematics and its applications}}, publisher = {Academic}, title = {Applications of negative dimensional tensors}, year = {1971}, address = {New York}, editor = {Welsh, D. J. A.}, isbn = {9780127433509}, pages = {221--244}, url = {http://homepages.math.uic.edu/~kauffman/Penrose.pdf}, } @Article{percgl, author = {A. V. Porubov and M. G. Velarde}, title = {Exact periodic solutions of the complex {Ginzburg-Landau} equation}, journal = {J. Math. Phys.}, year = {1999}, volume = {40}, pages = {884}, doi = {10.1063/1.532692}, } @Article{percol, author = {M. V. {\'E}ntin and G. M. {\'E}ntin}, journal = {Sov. Phys. JETP Lett.}, title = {Scale invariance in percolation theory and fractals}, year = {1996}, pages = {467}, volume = {64}, doi = {10.1134/1.567213}, } @Book{perko91, title = {{Differential Equations and Dynamical Systems}}, publisher = {Springer}, year = {1991}, author = {L. Perko}, address = {New York}, doi = {10.1007/978-1-4684-0392-3}, } @Book{PerRich82, author = {I. Percival and D. Richards}, publisher = {Cambridge Univ. Press}, title = {{Introduction to Dynamics}}, year = {1982}, address = {Cambridge}, isbn = {9780521281492}, doi = {10.1119/1.13560}, } @Article{PerViv, Title = {A linear code for the sawtooth and cat maps}, Author = {I. Percival and F. Vivaldi}, Journal = {Physica D}, Year = {1987}, Pages = {373--386}, Volume = {27}, DOI = {10.1016/0167-2789(87)90037-6} } @Article{Pesin74, Title = {Example of a nonergodic flow with nonzero characteristic numbers}, Author = {Pesin, Ya. B.}, Journal = {Funct. Anal. Appl.}, Year = {1974}, Pages = {263--264}, Volume = {8}, DOI = {10.1007/BF01075704} } @Article{Pesin77, Title = {Characteristic {Lyapunov} exponents and smooth ergodic theory}, Author = {Ya. B. Pesin}, Journal = {Russian Math. Surveys}, Year = {1977}, Pages = {55--114}, Volume = {32}, DOI = {10.1070/RM1977v032n04ABEH001639} } @Article{Pesin92, author = {Pesin, Ya . B.}, journal = {Ergod. Theor. Dynam. Syst.}, title = {Dynamical systems with generalized hyperbolic attractors: hyperbolic, ergodic and topological properties}, year = {1992}, pages = {123--151}, volume = {12}, doi = {10.1017/S0143385700006635}, } @Article{PetCorBol06, Title = {Symbolic dynamics of coupled map lattices}, Author = {Pethel, S. D. and Corron, N. J. and Bollt, E.}, Journal = {Phys. Rev. Lett.}, Year = {2006}, Pages = {034105}, Volume = {96}, DOI = {10.1103/PhysRevLett.96.034105} } @Article{PetCorBol07, Title = {Deconstructing spatiotemporal chaos using local symbolic dynamics}, Author = {Pethel, S. D. and Corron, N. J. and Bollt, E.}, Journal = {Phys. Rev. Lett.}, Year = {2007}, Pages = {214101}, Volume = {99}, DOI = {10.1103/PhysRevLett.99.214101} } @Book{Peterson, title = {{Ergodic Theory}}, publisher = {Cambridge Univ. Press}, year = {1990}, author = {K. Peterson}, isbn = {9780521389976}, address = {Cambridge UK}, } @Book{PetTri09, title = {{Applications of Group Theory in Quantum Mechanics}}, publisher = {Dover}, year = {2009}, author = {Petrashen, M. I. and Trifonov, E. D.}, isbn = {9780486472232}, address = {New York}, doi = {10.1063/1.3022793}, } @Article{pexp, Title = {Periodic orbit expansions for classical smooth flows}, Author = {P. Cvitanovi{\'c} and B. Eckhardt}, Journal = {J. Phys. A}, Year = {1991}, Pages = {L237}, Volume = {24}, DOI = {10.1088/0305-4470/24/5/005} } @Book{Peyret02, author = {R. Peyret}, publisher = {Springer}, title = {{Spectral Methods for Incompressible Flows}}, year = {2002}, address = {New York}, } @Book{PG97, author = {P. Gaspard}, publisher = {Cambridge Univ. Press}, title = {{Chaos, Scattering and Statistical Mechanics}}, year = {1998}, address = {Cambridge UK}, doi = {10.1017/cbo9780511628856}, } @Article{HBA94, author = {Hakmi, A. and Bosco, F. and Antoniou, I.}, title = {First return map of the periodic {Lorentz} gas}, journal = {Phys. Rev. E}, year = {1995}, volume = {51}, pages = {3952--3956}, doi = {10.1103/PhysRevE.51.3952}, } @Article{PhysToday04, author = {R. Fitzgerald}, title = {New experiments set the scale for the onset of turbulence in pipe flow}, journal = {Phys. Today}, year = {2004}, volume = {57}, pages = {21--23}, doi = {10.1063/1.1688059}, } @Article{PhysWorld04, author = {C. Barenghi}, journal = {Phys. World}, title = {Turbulent transition for fluids}, year = {2004}, volume = {17}, doi = {10.1088/2058-7058/17/12/25}, } @Article{pimsimp, author = {P. Moresco and S. P. Dawson}, title = {The {PIM}-simplex method: an extension of the {PIM}-triple method to saddles with an arbitrary number of expanding directions}, journal = {Physica}, year = {1999}, volume = {126D}, pages = {38}, doi = {10.1016/s0167-2789(98)00234-6}, } @Article{pimstag, Title = {Stagger-and-step method: {Detecting} and computing chaotic saddles in higher dimensions}, Author = {D. Sweet and H. E. Nusse. and J. A. Yorke}, Journal = {Phys. Rev. Lett.}, Year = {2001}, Pages = {2261--2264}, Volume = {86}, DOI = {10.1103/PhysRevLett.86.2261} } @Article{pimyk, author = {H. E. Nusse and J. A. Yorke}, title = {A procedure for finding numerical trajectories on chaotic saddles}, journal = {Physica D}, year = {1989}, volume = {36}, pages = {137--156}, doi = {10.1016/0167-2789(89)90253-4}, } @Article{Pinho2009, author = {Pinho, A. J. and Ferreira, P. J. S. G. and Garcia, S. P. and Rodrigues, J. M. O. S.}, journal = {BMC Bioinformatics}, title = {On finding minimal absent words}, year = {2009}, pages = {1--11}, volume = {10}, doi = {10.1186/1471-2105-10-137}, } @Book{PJD, author = {P. J. Davis}, publisher = {Amer. Math. Soc.}, title = {{Circulant Matrices}}, year = {1979}, address = {New York}, edition = {2}, isbn = {978-0821891650}, doi = {10.2307/2006411}, } @Article{Plemelj1909, Title = {{Zur Theorie der Fredholmschen Funktionalgleichung}}, Author = {Plemelj, J.}, Journal = {Monat. Math. Phys.}, Year = {1904}, Pages = {93--28}, Volume = {15}, DOI = {10.1007/BF01692293} } @Article{PlSiFi91, Title = {An investigation of chaotic {Kolmogorov} flows}, Author = {Platt, N. and Sirovich, L. and Fitzmaurice, N.}, Journal = {Phys. Fluids A}, Year = {1991}, Pages = {681--696}, Volume = {3}, DOI = {10.1063/1.858074} } @Article{PoBaGr88, author = {A. Politi and R. Badii and P. Grassberger}, title = {On the geometric structure of non-hyperbolic attractors}, journal = {J. Phys. A}, year = {1988}, volume = {21}, pages = {L763--L769}, doi = {10.1088/0305-4470/21/15/004}, } @Article{PoGiYaMa06, author = {Politi, A. and Ginelli, F. and Yanchuk, S. and Maistrenko, Y.}, journal = {Physica D}, title = {From synchronization to {Lyapunov} exponents and back}, year = {2006}, pages = {90--101}, volume = {224}, doi = {10.1016/j.physd.2006.09.032}, } @Article{Poinc1896, Title = {Sur les solutions p{\'e}riodiques et le principe de moindre action}, Author = {H. Poincar{\'e}}, Journal = {C. R. Acad. Sci. Paris}, Year = {1896}, Pages = {915--918}, Volume = {123} } @Book{poincare, Title = {{Les M{\'e}thodes Nouvelles de la M{\'e}chanique C{\'e}leste}}, Author = {H. Poincar{\'e}}, Publisher = {Guthier-Villars}, Year = {1899}, Address = {Paris} } @Book{poinper, Title = {{New Methods in Celestial Mechanics}}, Author = {H. Poincar{\'e}}, Publisher = {Springer}, Year = {1992}, Address = {New York} } @Article{PoKno05, Title = {Dynamics in the 1:2~{s}patial resonance with broken reflection symmetry}, Author = {J. Porter and E. Knobloch}, Journal = {Physica D}, Year = {2005}, Pages = {318--344}, Volume = {201}, DOI = {10.1016/j.physd.2005.01.001} } @InProceedings{Poll-1, Title = {Periodic orbits and zeta functions}, Author = {M. Pollicott}, Booktitle = {1999 AMS Summer Institute on {Smooth ergodic theory and applications}, Seattle}, Year = {1999}, Series = {Symposia Pure Applied Math.} } @Misc{Poll1206, Title = {The case of {Pollock}'s fractals focuses on physics}, Author = {Kennedy, R.}, HowPublished = {New York Times, Dec. 2, 2006}, URL = {http://www.nytimes.com/2006/12/02/books/02frac.html} } @Article{polli, Title = {Meromorphic extensions of generalised zeta functions}, Author = {Pollicott, M.}, Journal = {Inv. Math.}, Year = {1986}, Pages = {147--164}, Volume = {85}, DOI = {10.1007/BF01388795} } @Incollection{Pollicott02, author = {M. Pollicott}, title = {Periodic orbits and zeta functions}, booktitle = {{Handbook of Dynamical Systems}}, publisher = {Elsevier}, year = {2002}, editor = {Hasselblatt, B. and Katok, A.}, volume = {1, Part A}, pages = {409--452}, address = {New York}, doi = {10.1016/S1874-575X(02)80007-8}, } @Article{Pollicott85, Title = {On the rate of mixing of {Axiom A} flows}, Author = {Pollicott, M.}, Journal = {Inv. Math.}, Year = {1985}, Pages = {413--426}, Volume = {81}, DOI = {10.1007/BF01388579} } @Article{Pollicott91, Title = {A note on the {Artuso-Aurell-Cvitanovi{\'c}} approach to the {Feigenbaum} tangent operator}, Author = {Pollicott, M.}, Journal = {J. Stat. Phys.}, Year = {1991}, Pages = {257--267}, Volume = {62}, DOI = {10.1007/BF01020869} } @Book{Pollicott93, author = {Pollicott, M.}, publisher = {Cambridge Univ. Press}, title = {{Lectures on Ergodic Theory and Pesin Theory on Compact Manifolds}}, year = {1993}, address = {Cambridge UK}, doi = {10.1017/cbo9780511752537}, } @Article{PollJ-Sm06, Title = {Fractal analysis: {Revisiting Pollock's} drip paintings}, Author = {Jones-Smith, K. and Mathur, H.}, Journal = {Nature}, Year = {2006}, Pages = {E9--E10}, Volume = {444}, DOI = {10.1038/nature05398} } @Article{PollTay06, author = {Taylor, R. P. and Micolich, A. P. and Jonas, D.}, title = {Fractal analysis: {Revisiting Pollock's} drip paintings {(Reply)}}, journal = {Nature}, year = {2006}, volume = {444}, pages = {E10--E11}, doi = {10.1038/nature05399}, } @Article{PollTay99, Title = {Fractal analysis of {Pollock}'s drip paintings}, Author = {Taylor, R. P. and Micolich, A. P. and Jonas, D.}, Journal = {Nature}, Year = {1999}, Pages = {422--422}, Volume = {399}, DOI = {10.1038/20833} } @Article{PolPuc92, author = {A. Politi and G. P. Puccioni}, title = {Invariant measure in coupled maps}, journal = {Physica D}, year = {1992}, volume = {58}, pages = {384--391}, doi = {10.1016/0167-2789(92)90124-6}, } @Article{Pomeau80, author = {Pomeau, Y. and Manneville, P.}, journal = {Commun. Math. Phys.}, title = {Intermittent transition to turbulence in dissipative dynamical systems}, year = {1980}, pages = {189}, volume = {74}, doi = {10.1007/BF01197757}, } @Book{popebook, author = {S. B. Pope}, publisher = {Cambridge Univ. Press}, title = {{Turbulent Flows}}, year = {2000}, address = {Cambridge UK}, doi = {10.1017/cbo9780511840531}, } @Article{postgal89, author = {B. Garc\'{i}a-Archilla and J. Novo and E. S. Titi}, title = {Postprocessing the {G\"{a}lerkin} method: {A} novel approach to approximate inertial manifolds}, journal = {SIAM J. Numer. Anal.}, year = {1998}, volume = {35}, pages = {941--972}, doi = {10.1137/s0036142995296096}, } @Article{PoToLe98, Title = {{Lyapunov} exponents from node-counting arguments}, Author = {A. Politi and A. Torcini and S. Lepri}, Journal = {J. Phys. IV}, Year = {1998}, Pages = {263--270}, Volume = {8}, DOI = {10.1051/jp4:1998636} } @Book{PoYu, author = {Pollicott, M. and Yuri, M.}, publisher = {Cambridge Univ. Press}, title = {Dynamical systems and ergodic theory}, year = {1998}, address = {Cambridge UK}, doi = {10.1017/cbo9781139173049}, } @Article{PP83, author = {W. Parry and M. Pollicott}, title = {An analogue of the prime number theorem for closed orbits of {Axiom A} flows}, journal = {Ann. Math.}, year = {1983}, volume = {118}, pages = {573--591}, url = {http://www.jstor.org/stable/2006982} } @Book{PP90, Title = {{Zeta Functions and the Periodic Orbit Structure of Hyperbolic Dynamics}}, Author = {Parry, W. and Pollicott, M.}, Publisher = {Ast{\'e}risque, Soc. Math. France}, Year = {1990}, URL = {http://smf4.emath.fr/en/Publications/Asterisque/1990/187-188/html/smf_ast_187-188.html}, Volume = {187--188} } @Book{PPRS92, title = {{Encounter with Chaos - {Self} Organised Hierarchical Complexity in Semiconductor Experiments}}, publisher = {Springer}, year = {1992}, author = {J. Peinke and J. Parisi and O. E. R{\"o}ssler and R. Stoop}, address = {New York}, doi = {10.1007/978-3-642-77625-0}, } @Article{pre88top, Title = {Topological and metric properties of {H{\'e}non}-type strange attractors}, Author = {Cvitanovi{\'c}, P. and Gunaratne, G. H. and Procaccia, I.}, Journal = {Phys. Rev. A}, Year = {1988}, Pages = {1503--1520}, Volume = {38}, DOI = {10.1103/PhysRevA.38.1503} } @Phdthesis{Prell, Title = {{Maps of the Interval with Indifferent Fixed Points: Thermodynamic Formalism and Phase Transitions}}, Author = {T. Prellberg}, School = {Virginia Polytechnic Inst.}, Year = {1991} } @Article{Prell93, Title = {Towards a complete determination of the spectrum of a transfer operator associated with intermittency}, Author = {T. Prellberg}, Journal = {J. Phys. A}, Year = {2003}, Pages = {2455}, Volume = {36}, DOI = {10.1088/0305-4470/36/10/306} } @Article{PrelSla92, Title = {Maps of intervals with indifferent fixed points: {Thermodynamic} formalism and phase transitions}, Author = {Prellberg, T. and Slawny, J.}, Journal = {J. Stat. Phys.}, Year = {1992}, Pages = {503--514}, Volume = {66}, DOI = {10.1007/BF01060077} } @Book{Press86, author = {Press, W. H. and Flannery, B. P. and Teukolsky, S. A. and Vetterling, W. T.}, publisher = {Cambridge Univ. Press}, title = {{Numerical Recipes}}, year = {2007}, address = {Cambridge UK}, edition = {3}, isbn = {9780521880688}, } @Book{Press96, author = {W. H. Press and B. P. Flannery and S. A. Teukolsky and W. T. Vetterling}, publisher = {Cambridge Univ. Press}, title = {{Numerical Recipes in {Fortran} 77}}, year = {1996}, address = {Cambridge UK}, edition = {2}, isbn = {9780521430647}, } @Article{Proctor88, author = {Proctor, R. A.}, title = {Odd symplectic groups}, journal = {Inv. Math.}, year = {1988}, volume = {92}, pages = {307--332}, doi = {10.1007/BF01404455} } @Article{Proctor93, author = {Proctor, R. A.}, title = {Reflection and algorithm proofs of some more {Lie} group dual pair identities}, journal = {J. Combin. Theory A}, year = {1993}, volume = {62}, pages = {107--127}, doi = {10.1016/0097-3165(93)90074-i}, } @Article{PSD01, author = {D. Pingel and P. Schmelcher and F. K. Diakonos}, title = {Detecting unstable periodic orbits in chaotic continuous-time dynamical systems}, journal = {Phys. Rev. E}, year = {2001}, volume = {64}, pages = {026214}, doi = {10.1103/physreve.64.026214}, } @Article{PSDB00, author = {Detlef Pingel and P. Schmelcher and F. K. Diakonos and O. Biham}, title = {Theory and applications of the systematic detection of unstable periodic orbits in dynamical systems}, journal = {Phys. Rev. E}, year = {2000}, volume = {62}, pages = {2119}, doi = {10.1103/physreve.62.2119}, } @Inproceedings{PSSTV02, author = {C. Polymilis and G. Servizi and Ch. Skokos and G. Turchetti and M. N. Vrahatis}, title = {Locating periodic orbits by {Topological Degree} theory}, booktitle = {{Libration Point Orbits and Applications}}, year = {2003}, address = {Singapore}, publisher = {World Scientific}, doi = {10.1142/9789812704849_0031}, } @Article{pugh67cl, author = {C. Pugh}, title = {An improved closing lemma and a general density theorem}, journal = {Amer. J. Math.}, year = {1967}, volume = {89}, doi = {10.2307/2373414}, } @Book{PuLev86, title = {{Qualitative Modeling of Complex Systems: An Introduction to Loop Analysis and Time Averaging}}, publisher = {Harvard Univ. Press}, year = {1985}, author = {Puccia, C. J. and Levins, R.}, isbn = {9780674741102}, doi = {10.4159/harvard.9780674435070}, } @PhdThesis{PutkaradzeThesis, author = {Putkaradze, V.}, title = {{Local Structures in Extended Systems}}, school = {Copenhagen Univ.}, year = {1997}, address = {Copenhagen}, url = {http://ChaosBook.org/projects/theses.html}, } @Article{R1883, author = {O. Reynolds}, title = {An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and the law of resistance in parallel channels}, journal = {Proc. R. Soc. Lond. A}, year = {1883}, volume = {174}, pages = {935--982}, doi = {10.1098/rstl.1883.0029}, } @Article{R1894, author = {Osborne Reynolds}, title = {On the dynamical theory of incompressible viscous flows and the determination of the criterion}, journal = {Proc. R. Soc. Lond. A}, year = {1894}, volume = {186}, pages = {123--161}, doi = {10.1098/rspl.1894.0075}, } @Article{RaHaAb96, author = {Rauh, A. and Hannibal, L. and Abraham, N. B.}, title = {Global stability properties of the complex {Lorenz} model}, journal = {Physica D}, year = {1996}, volume = {99}, pages = {45--58}, doi = {10.1016/s0167-2789(96)00129-7}, } @Book{Ramond10, author = {Ramond, P.}, publisher = {Cambridge Univ. Press}, title = {{Group Theory: A Physicist's Survey}}, year = {2010}, address = {Cambridge UK}, doi = {10.1017/cbo9780511781865}, } @Article{RamSri00, Title = {A comparative study of computation of {Lyapunov} spectra with different algorithms}, Author = {K. Ramasubramanian and M.S. Sriram}, Journal = {Physica D}, Year = {2000}, Pages = {72--86}, Volume = {139}, DOI = {10.1016/S0167-2789(99)00234-1} } @Article{Rand82, Title = {Dynamics and symmetry. {Predictions} for modulated waves in rotating fluids}, Author = {Rand, D.}, Journal = {Arch. Rational Mech. Anal.}, Year = {1982}, Pages = {1--37}, Volume = {79}, DOI = {10.1007/BF02416564} } @Article{Rayleigh13, Title = {{LXV. On} the motion of a viscous fluid}, Author = {Rayleigh, J. W. S.}, Journal = {Philos. Mag. Ser. 6}, Year = {1913}, Pages = {776--786}, Volume = {26}, DOI = {10.1080/14786441308635022} } @Book{Rayleigh1877I, Title = {{The Theory of Sound}}, Author = {Rayleigh, J. W. S.}, Publisher = {Macmillan}, Year = {1877}, Address = {London}, URL = {https://archive.org/details/theorysound06raylgoog}, Volume = {1} } @Book{Rayleigh1896II, title = {{The Theory of Sound}}, publisher = {Macmillan}, year = {1896}, author = {Rayleigh, J. W. S.}, volume = {2}, address = {London}, doi = {10.1063/1.3060230}, url = {https://archive.org/details/theoryofsound02raylrich}, } @Article{Rayleigh83, Title = {On the crispation of fluid resting upon vibrating support}, Author = {J. S. Rayleigh}, Journal = {Philos. Mag.}, Year = {1883}, Pages = {50--58}, Volume = {16}, URL = {https://archive.org/details/londonedinburg5161883lond} } @Article{rcd, author = {O. B. Isaeva and S. P. Kuznetsov}, title = {On scaling properties of two-dimensional maps near the accumulation point of the period-tripling cascade}, journal = {Regul. Chaotic Dyn.}, year = {2000}, volume = {5}, pages = {459--476}, url = {http://rcd.ics.org.ru/upload/iblock/484/RCD050406.pdf}, } @Article{RCLdisc, author = {J. M. Robbins and S. C. Creagh and R. G. Littlejohn}, title = {Complex periodic orbits in the rotational spectrum of molecules: {The} example of {${\mathrm{SF}}_{6}$}}, journal = {Phys. Rev. A}, year = {1989}, volume = {39}, pages = {2838--2854}, doi = {10.1103/PhysRevA.39.2838}, } @Article{RCMR04, author = {Rempel, E. L. and Chian, A. C. and Macau, E. E. and Rosa, R. R.}, title = {Analysis of chaotic saddles in high-dimensional dynamical systems: the {Kuramoto-Sivashinsky} equation}, journal = {Chaos}, year = {2004}, volume = {14}, pages = {545--56}, doi = {10.1063/1.1759297}, } @Article{ReChMi07, Title = {Chaotic saddles at the onset of intermittent spatiotemporal chaos}, Author = {Rempel, E. L. and Chian, A. C. and Miranda, R. A.}, Journal = {Phys. Rev. E}, Year = {2007}, Pages = {056217}, Volume = {76}, DOI = {10.1103/PhysRevE.76.056217} } @Article{ReCh05, author = {Rempel, E. L. and Chian, A. C.}, title = {Intermittency induced by attractor-merging crisis in the {Kuramoto-Sivashinsky} equation}, journal = {Phys. Rev. E}, year = {2005}, volume = {71}, pages = {016203}, doi = {10.1103/PhysRevE.71.016203}, } @Article{ReCh07, author = {Rempel, E. L. and Chian, A. C.}, title = {Origin of transient and intermittent dynamics in spatiotemporal chaotic systems}, journal = {Phys. Rev. Lett.}, year = {2007}, volume = {98}, pages = {014101}, doi = {10.1103/physrevlett.98.014101}, } @Article{reimann1, author = {P. Reimann}, title = {Noisy one-dimensional maps near a crisis 1: Weak {Gauss}ian white and colored noise}, journal = {J. Stat. Phys.}, year = {1996}, volume = {82}, pages = {1467--1501}, doi = {10.1007/bf02183392}, } @Article{reimann2, author = {P. Reimann}, title = {Noisy one-dimensional maps near a crisis 2: General uncorrelated weak noise}, journal = {J. Stat. Phys.}, year = {1996}, volume = {85}, pages = {403--425}, doi = {10.1007/bf02174212}, } @Book{Richter10, title = {{Semiclassical Theory of Mesoscopic Quantum Systems}}, publisher = {Springer}, year = {2000}, author = {Richter, K.}, isbn = {9783662156506}, address = {Berlin}, doi = {10.1007/bfb0109634}, url = {http://www.physik.uni-regensburg.de/forschung/richter/richter/pages/research/springer-tracts-161.pdf}, } @Article{Rink200331, Title = {Symmetric invariant manifolds in the {Fermi-Pasta-Ulam} lattice}, Author = {Bob Rink}, Journal = {Physica D}, Year = {2003}, Pages = {31--42}, Volume = {175}, DOI = {10.1016/S0167-2789(02)00694-2} } @Book{riordan, author = {J. Riordan}, publisher = {Wiley}, title = {{An Introduction to Combinatorial Analysis}}, year = {1958}, address = {New York}, doi = {10.1515/9781400854332}, } @Book{Risken96, title = {{The {Fokker-Planck} Equation}}, publisher = {Springer}, year = {1996}, author = {H. Risken and H. Haken}, address = {New York}, doi = {10.1007/978-3-642-61544-3_4}, } @Article{RK02, Title = {{Lyapunov} instability for a periodic {Lorentz} gas thermostated by deterministic scattering}, Author = {Rateitschak, K. and Klages, R.}, Journal = {Phys. Rev. E}, Year = {2002}, Pages = {036209}, Volume = {65}, DOI = {10.1103/PhysRevE.65.036209} } @Book{RKbook07, title = {{Microscopic Chaos, Fractals and Transport in Nonequilibrium Statistical Mechanics}}, publisher = {World Scientific}, year = {2007}, author = {R. Klages}, address = {Singapore}, isbn = {978-981-256-507-5}, doi = {10.1142/9789812771513}, } @Book{RKdiss, title = {{Deterministic Diffusion in One-dimensional Chaotic Dynamical Systems}}, publisher = {Wissenschaft and Technik-Verlag}, year = {1996}, author = {R. Klages}, address = {Berlin}, url = {http://www.maths.qmul.ac.uk/~klages/publ/phd.html}, } @Article{RLCS95, Title = {A {Newton-Picard} shooting method for computing periodic solutions of large-scale dynamical systems}, Author = {D. Roose and K. Lust and A. Champneys and A. Spence}, Journal = {Chaos Solit. Fract.}, Year = {1995}, Pages = {1913--1925}, Volume = {5}, DOI = {10.1016/0960-0779(95)90873-Q} } @Article{RM97, Title = {Thermostatted {N}-particle systems and orbital measures}, Author = {L. Rondoni and G. P. Morriss}, Journal = {Phys. Rep.}, Year = {1997}, Pages = {173--181}, Volume = {290}, DOI = {10.1016/S0370-1573(97)00066-5} } @InCollection{RMChaosHist, author = {R. Mainieri and P. Cvitanovi{\'c}}, title = {A brief history of chaos}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2020}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/paper.shtml#appendHist}, } @InProceedings{RMLNC94, Title = {Lorentz gas, periodic orbit expansions, partitions, and ergodicity}, Author = {Rondoni, L. and G. P. Morriss and J. P. Lloyd and M. Niemeyer and E. G. D. Cohen}, Booktitle = {ICDC, Tokyo 1994}, Year = {1994}, DOI = {10.1063/1.166139} } @Article{Ro88, author = {Roekaerts, D.}, title = {{Painlev{\'e}} property and constants of the motion of the complex {Lorenz} model}, journal = {J. Phys. A}, year = {1988}, volume = {21}, pages = {L495--L498}, doi = {10.1088/0305-4470/21/9/003}, } @Article{robb, Title = {Discrete symmetries in periodic-orbit theory}, Author = {J. M. Robbins}, Journal = {Phys. Rev. A}, Year = {1989}, Pages = {2128--2136}, Volume = {40}, DOI = {10.1103/PhysRevA.40.2128} } @Book{RobertsStewart2006, title = {{Singularity Theory and its Applications: Warwick 1989, Part II: Singularities, Bifurcations and Dynamics}}, publisher = {Springer Berlin Heidelberg}, year = {2006}, author = {Roberts, M. and Stewart, I.}, isbn = {9783540470472}, series = {Lecture Notes in Mathematics}, } @Book{Robinson12, Title = {{An Introduction to Dynamical Systems: Continuous and Discrete}}, Author = {Robinson, R. C.}, Publisher = {Amer. Math. Soc.}, Year = {2012}, Address = {New York}, ISBN = {9780821891353} } @Article{Robinson1995, Title = {Finite-dimensional behavior in dissipative partial differential equations}, Author = {Robinson, J. C.}, Journal = {Chaos}, Year = {1995}, Pages = {330--345}, Volume = {5}, DOI = {10.1063/1.166081} } @Article{Robinson91, author = {S. K. {Robinson}}, title = {Coherent motions in the turbulent boundary layer}, journal = {Ann. Rev. Fluid Mech.}, year = {1991}, volume = {23}, pages = {601--639}, doi = {10.1146/annurev.fluid.23.1.601}, } @Article{RobQui92, author = {J. A. G. Roberts and G. R. W. Quispel}, title = {Chaos and time-reversal symmetry. {Order} and chaos in reversible dynamical systems}, journal = {Phys. Rep.}, year = {1992}, volume = {216}, pages = {63--177}, doi = {10.1016/0370-1573(92)90163-T} } @Article{ROD1977329, Title = {Hyperbolic periodic orbits}, Author = {D. L. Rod and G Pecelli and R. C. Churchill}, Journal = {J. Diff. Eqn.}, Year = {1977}, Pages = {329--348}, Volume = {24}, DOI = {10.1016/0022-0396(77)90003-1} } @Article{Rod73, author = {D. L. Rod}, title = {Pathology of invariant sets in the monkey saddle}, journal = {J. Diff. Eqn.}, year = {1973}, volume = {14}, pages = {129--170}, doi = {10.1016/0022-0396(73)90082-X}, } @Article{Romanov73, author = {V. A. Romanov}, title = {Stability of plane-parallel {Couette} flow}, journal = {Funct. Anal. Appl.}, year = {1973}, volume = {7}, pages = {137--146}, doi = {10.1007/bf01078886}, } @Article{Rome69, author = {Rome, H.}, title = {A direct solution to the linear variance equation of a time-invariant linear system}, journal = {IEEE Trans. Automatic Control}, year = {1969}, volume = {14}, pages = {592--593}, doi = {10.1109/tac.1969.1099271}, } @Article{RomKed90, author = {V. Rom-Kedar}, title = {Transport rates of a class of two-dimensional maps and flows}, journal = {Physica D}, year = {1990}, volume = {43}, pages = {229--268}, doi = {10.1016/0167-2789(90)90135-C}, } @Article{Ronc95, Title = {Small-fluctuation expansion of the transition probability for a diffusion process}, Author = {M. Roncadelli}, Journal = {Phys. Rev. E}, Year = {1995}, Pages = {4661}, Volume = {52}, DOI = {10.1103/PhysRevE.52.4661} } @Article{RonCoh98, Title = {Orbital measures in non-equilibrium statistical mechanics: the {Onsager} relations}, Author = {L. Rondoni and E. G. D. Cohen}, Journal = {Nonlinearity}, Year = {1998}, Pages = {1395--1406}, Volume = {11}, DOI = {10.1088/0951-7715/11/5/013} } @Article{RoSa00, author = {Roweis, S. T. and Saul, L. K.}, title = {Nonlinear dimensionality reduction by locally linear embedding}, journal = {Science}, year = {2000}, volume = {290}, pages = {2323--2326}, doi = {10.1126/science.290.5500.2323}, } @Article{Rosalie14, Title = {Template of two foliated attractors--{Lorenz and Chen} systems}, Author = {Rosalie, M.}, Journal = {Int. J. Bifur. Chaos}, Year = {2016}, Pages = {1650037}, Volume = {26}, DOI = {10.1142/S0218127416500371} } @PhdThesis{RosenqvThesis, author = {E. Rosenqvist}, school = {Copenhagen Univ.}, title = {{Periodic Orbit Theory Beyond Semiclassics: {Convergence}, Diffraction and {$\hbar$} Corrections}}, year = {1995}, address = {Copenhagen}, url = {http://ChaosBook.org/projects/theses.html}, } @Article{ross, author = {O. E. R{\"{o}}ssler}, title = {An equation for continuous chaos}, journal = {Phys. Lett. A}, year = {1976}, volume = {57}, pages = {397}, doi = {10.1016/0375-9601(76)90101-8}, } @Article{roth99, Title = {Persistent patterns in transient chaotic fluid mixing}, Author = {D. Rothstein and E. Henry and J. P. Gollub}, Journal = {Nature}, Year = {1999}, Pages = {770--772}, Volume = {401}, DOI = {10.1038/44529} } @Misc{Rothman06, author = {D. Rothman}, title = {{Nonlinear Dynamics I: Chaos}}, year = {2006}, institution = {MIT OpenCourseWare}, url = {https://dspace.mit.edu/bitstream/handle/1721.1/84612/12-006j-fall-2006/contents/index.htm}, } @Article{rowley_reconstruction_2000, Title = {Reconstruction equations and the {Karhunen-Lo{\'e}ve} expansion for systems with symmetry}, Author = {Rowley, C. W. and Marsden, J. E.}, Journal = {Physica D}, Year = {2000}, Pages = {1--19}, Volume = {142}, DOI = {10.1016/S0167-2789(00)00042-7} } @Article{rowley_reduction_2003, Title = {Reduction and reconstruction for self-similar dynamical systems}, Author = {Rowley, C. W. and Kevrekidis, I. G. and Marsden, J. E. and Lust, K.}, Journal = {Nonlinearity}, Year = {2003}, Pages = {1257--1275}, Volume = {16}, DOI = {10.1088/0951-7715/16/4/304} } @Article{Rowley05, Title = {Model reduction for fluids, using balanced proper orthogonal decomposition}, Author = {Rowley, C. W.}, Journal = {Int. J. Bifur. Chaos}, Year = {2005}, Pages = {997--1013}, Volume = {15}, DOI = {10.1142/S0218127405012429}, } @Article{RS01, Title = {Analysis of chaotic motion and its shape dependence in a generalized piecewise linear map}, Author = {Rajagopalan, S. and Sabir, M.}, Journal = {Phys. Rev. E}, Year = {2001}, Pages = {057201}, Volume = {63}, DOI = {10.1103/PhysRevE.63.057201} } @Article{RSBH98, author = {S. C. Reddy and P. J. Schmid and J. S. Baggett and D. S. Henningson}, title = {On stability of streamwise streaks and transition thresholds in plane channel flows}, journal = {J. Fluid Mech.}, year = {1998}, volume = {365}, pages = {269--303}, doi = {10.1017/s0022112098001323}, } @Article{RSW90, Title = {A breathing chaos}, Author = {P. H. Richter and H.-J. Scholz and A. Wittek}, Journal = {Nonlinearity}, Year = {1990}, Pages = {45--67}, Volume = {1}, DOI = {10.1088/0951-7715/3/1/004} } @Book{rtb, title = {{Theory of Orbits}}, publisher = {Academic}, year = {1967}, author = {V. Szebehely}, address = {New York}, isbn = {9780323143462}, } @Article{Rudnicki15, Title = {An ergodic theory approach to chaos}, Author = {Rudnicki, R.}, Journal = {Discrete Contin. Dyn. Syst.}, Year = {2015}, Pages = {757--770}, Volume = {35}, DOI = {10.3934/dcds.2015.35.757} } @Article{rue, Title = {Generalized zeta-functions for {Axiom A} basic sets}, Author = {D. Ruelle}, Journal = {Bull. Amer. Math. Soc.}, Year = {1976}, Pages = {153--156}, Volume = {82}, DOI = {10.1090/S0002-9904-1976-14003-7} } @Article{rue04ne, author = {D. Ruelle}, title = {Conversations on nonequilibrium physics with an extraterrestrial}, journal = {Phys. Today}, year = {2004}, volume = {57}, pages = {48--53}, doi = {10.1063/1.1768674}, } @Article{rue68, Title = {Statistical mechanics of a one-dimensional lattice gas}, Author = {D. Ruelle}, Journal = {Commun. Math. Phys.}, Year = {1968}, Pages = {267--288}, Volume = {9}, DOI = {10.1007/BF01654281} } @Article{Rue76, author = {D. Ruelle}, title = {A measure associated with {Axiom-A} attractors}, journal = {Amer. J. Math.}, year = {1976}, volume = {98}, pages = {619--654}, doi = {10.2307/2373810}, } @Article{rue87a, Title = {Resonances for {Axiom A} flows}, Author = {D. Ruelle}, Journal = {J. Diff. Geom.}, Year = {1987}, Pages = {99--116}, Volume = {25}, URL = {http://projecteuclid.org/euclid.jdg/1214440726} } @Article{rue87b, Title = {One-dimensional {Gibbs} states and {Axiom A} diffeomorphisms}, Author = {D. Ruelle}, Journal = {J. Diff. Geom.}, Year = {1987}, Pages = {117--137}, Volume = {25}, URL = {http://projecteuclid.org/euclid.jdg/1214440727} } @Article{rue89, Title = {The thermodynamic formalism for expanding maps}, Author = {D. Ruelle}, Journal = {Commun. Math. Phys.}, Year = {1989}, Pages = {239--262}, Volume = {125}, DOI = {10.1007/BF01217908} } @Article{ruel83, author = {D. Ruelle}, title = {Flots qui ne m{\'e}langent pas exponentiellement}, journal = {C. R. Acad. Sci. Paris S{\'e}r. I Math}, year = {1983}, volume = {296}, pages = {191--193}, doi = {10.1142/9789812833709_0024}, } @Article{ruelext, author = {D. Ruelle}, title = {Large volume limit of the distribution of characteristic exponents in turbulence}, journal = {Commun. Math. Phys.}, year = {1982}, volume = {87}, pages = {287--302}, doi = {10.1007/BF01218566}, } @Article{ruell71, author = {D. Ruelle and F. Takens}, title = {On the nature of turbulence}, journal = {Commun. Math. Phys.}, year = {1971}, volume = {20}, pages = {167}, doi = {10.1007/bf01646553}, } @Article{ruell73, Title = {Bifurcations in presence of a symmetry group}, Author = {D. Ruelle}, Journal = {Arch. Rational Mech. Anal.}, Year = {1973}, Pages = {136--152}, Volume = {51}, DOI = {Bifurcations in presence of a symmetry group} } @Book{ruelle, author = {D. Ruelle}, publisher = {Cambridge Univ. Press}, title = {{Thermodynamic Formalism: The Mathematical Structure of Equilibrium Statistical Mechanics}}, year = {2004}, address = {Cambridge UK}, edition = {2}, doi = {10.1017/cbo9780511617546}, } @Article{Ruelle:68, Title = {Statistical mechanics of a one-dimensional lattice gas}, Author = {D. Ruelle}, Journal = {Commun. Math. Phys.}, Year = {1968}, Pages = {267--288}, Volume = {9}, DOI = {10.1007/BF01654281} } @Article{Ruelle09, Title = {A review of linear response theory for general differentiable dynamical systems}, Author = {D. Ruelle}, Journal = {Nonlinearity}, Year = {2009}, Pages = {855--870}, Volume = {22}, DOI = {10.1088/0951-7715/22/4/009} } @Article{Ruelle72, Title = {Statistical mechanics on a compact set with {$Z^\nu $} action satisfying expansiveness and specification}, Author = {D. Ruelle}, Journal = {Bull. Amer. Math. Soc.}, Year = {1972}, Pages = {988--991}, Volume = {78}, DOI = {10.1090/S0002-9904-1972-13078-7} } @Article{Ruelle73, Title = {Statistical mechanics on a compact set with {$ Z^{v}$} action satisfying expansiveness and specification}, Author = {D. Ruelle}, Journal = {Trans. Amer. Math. Soc.}, Year = {1973}, Pages = {237--251}, Volume = {185}, DOI = {10.1090/S0002-9947-1973-0417391-6} } @Article{Ruelle76, author = {D. Ruelle}, title = {Zeta-functions for expanding maps and {Anosov} flows}, journal = {Inv. Math.}, year = {1976}, volume = {34}, pages = {231--242}, doi = {10.1007/bf01403069}, } @Article{Ruelle76a, Title = {Generalized zeta-functions for {Axiom A} basic sets}, Author = {D. Ruelle}, Journal = {Bull. Amer. Math. Soc.}, Year = {1976}, Pages = {153--156}, Volume = {82}, DOI = {10.1090/S0002-9904-1976-14003-7} } @Article{ruelle79, author = {D. Ruelle}, title = {Ergodic theory of differentiable dynamical systems}, journal = {Publ. Math. IHES}, year = {1979}, volume = {50}, pages = {275}, doi = {10.1007/bf02684768}, } @Article{ruelle86, Title = {Locating resonances for {Axiom A} dynamical systems}, Author = {Ruelle, D.}, Journal = {J. Stat. Phys.}, Year = {1986}, Pages = {281--292}, Volume = {44}, DOI = {10.1007/BF01011300} } @Article{Ruelle90, Title = {An extension of the theory of {Fredholm} determinants}, Author = {D. Ruelle}, Journal = {Inst. Hautes \'Etudes Sci. Publ. Math.}, Year = {1990}, Pages = {175--193}, Volume = {72}, DOI = {10.1007/BF02699133} } @Article{Ruelle90a, author = {Ruelle, D.}, title = {The {Deterministic} chaos: the science and the fiction}, journal = {Proc. R. Soc. Lond. A}, year = {1990}, volume = {427}, pages = {241--248}, doi = {10.1098/rspa.1990.0010}, } @InProceedings{Ruelle91, author = {D. Ruelle}, booktitle = {{Mathematical Physics X}}, title = {Dynamical zeta functions: {Where} do they come from and what are they good for?}, year = {1992}, address = {Berlin}, pages = {43--51}, publisher = {Springer}, doi = {10.1007/978-3-642-77303-7_4}, } @Techreport{Ruelle95, Title = {Functional determinants related to dynamical systems and the thermodynamic formalism}, Author = {Ruelle, D.}, Institution = {Inst. Hautes Etud. Sci.}, Year = {1995}, Address = {Bures-sur-Yvette}, Number = {IHES-P-95-30}, URL = {http://cds.cern.ch/record/281769} } @Article{Ruelle96, author = {Ruelle, D.}, journal = {Commun. Math. Phys.}, title = {Functional equation for dynamical zeta functions of {Milnor-Thurston} type}, year = {1996}, pages = {63--88}, volume = {175}, doi = {10.1007/BF02101624}, } @Article{Rug99, Title = {Intermittency and regularized {Fredholm} determinants}, Author = {H. H. Rugh}, Journal = {Inv. Math.}, Year = {1999}, Pages = {1--24}, Volume = {135}, DOI = {10.1007/s002220050277} } @PhdThesis{RughThesis, author = {Rugh, H. H.}, title = {{Time Evoluation and Correlations in Chaotic Dynamical Systems}}, school = {Univ. of Copenhagen}, year = {1992}, address = {Copenhagen}, } @Incollection{RumSch01, Title = {The orbit space method: theory and application}, Author = {M. Rumberger and J. Scheurle}, Booktitle = {Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems}, Publisher = {Springer}, Year = {2001}, Address = {New York}, Editor = {B. Fiedler}, URL = {http://dynamics.mi.fu-berlin.de/danse/} } @Article{rw, Title = {Calculation of turbulent diffusion for the {Chirikov-Taylor} model}, Author = {A. B. Rechester and R. B. White}, Journal = {Phys. Rev. Lett.}, Year = {1980}, Pages = {1586--1589}, Volume = {44}, DOI = {10.1103/PhysRevLett.44.1586} } @Article{rwwCreep, author = {P. E. Rosenqvist and N. D. Whelan and A. Wirzba}, title = {Small disks and semiclassical resonances}, journal = {J. Phys. A}, year = {1996}, volume = {29}, pages = {5441--5453}, doi = {10.1088/0305-4470/29/17/018}, } @Article{Ryskin97, Title = {Simple procedure for correcting equations of evolution: {Application to Markov} processes}, Author = {Ryskin, G.}, Journal = {Phys. Rev. E}, Year = {1997}, Pages = {5123--5127}, Volume = {56}, DOI = {10.1103/PhysRevE.56.5123} } @Book{SaCa, Title = {{Numerical {Hamiltonian} problems}}, Author = {J. M. Sanz-Serna and M. P. Calvo}, Publisher = {Chapman and Hall}, Year = {1994}, Address = {London UK} } @InProceedings{SadoEfst05, author = {D.A. Sadovski and K. Efstathiou}, booktitle = {{Geometric Mechanics and Symmetry: the Peyresq Lectures}}, title = {No polar coordinates}, year = {2005}, address = {Cambridge UK}, editor = {J. Montaldi and T. Ratiu}, pages = {211--302}, publisher = {Cambridge Univ. Press}, doi = {10.1002/0471743984.vse5659}, } @Article{saka90br, Title = {Breakdown of the phase dynamics}, Author = {H. Sakaguchi}, Journal = {Progr. Theor. Phys.}, Year = {1990}, Pages = {792--800}, Volume = {84}, DOI = {10.1143/ptp/84.5.792} } @Inproceedings{Sakella12, author = {Sakellariadou, M.}, title = {Noncommutative spectral geometry: {A} guided tour for theoretical physicists}, booktitle = {{Proc. Corfu Summer Institute 2011 }}, year = {2011}, editor = {G. Zoupanos}, volume = {CORFU2011}, pages = {053}, publisher = {PoS}, url = {http://pos.sissa.it/cgi-bin/reader/contribution.cgi?id=155/053}, } @Book{Sakita85, title = {{Quantum Theory of Many-variable Systems and Fields}}, publisher = {World Scientific}, year = {1985}, author = {Sakita, B.}, isbn = {9789971978570}, doi = {10.1142/0163}, } @Article{SakStaVit11, Title = {Noncommutative spectral geometry, algebra doubling, and the seeds of quantization}, Author = {Sakellariadou, M. and Stabile, A. and Vitiello, G.}, Journal = {Phys. Rev. D}, Year = {2011}, Pages = {045026}, Volume = {84}, DOI = {10.1103/PhysRevD.84.045026} } @Article{SakWhe03, author = {J. Sakhr and N. D. Whelan}, title = {Semiclassical trace formulas for noninteracting identical particles}, journal = {Phys. Rev. E}, year = {2003}, volume = {67}, pages = {066213}, doi = {10.1103/physreve.67.066213}, } @Book{sal, author = {A. Salomaa}, publisher = {Academic}, title = {{Formal Languages}}, year = {1973}, address = {San Diego}, isbn = {0-12-615750-2}, } @Article{saltzman1962, author = {B. Saltzman}, title = {Finite amplitude free convection as an initial value problem}, journal = {J. Atmos. Sci.}, year = {1962}, volume = {19}, pages = {329--341}, doi = {10.1175/1520-0469(1962)019<0329:fafcaa>2.0.co;2}, } @Article{Sanders05, Title = {Fine structure of distributions and central limit theorem in diffusive billiards}, Author = {Sanders, D. P.}, Journal = {Phys. Rev. E}, Year = {2005}, Pages = {016220}, Volume = {71}, DOI = {10.1103/PhysRevE.71.016220} } @Article{SaRo02, Title = {Think globally, fit locally: {Unsupervised} learning of low dimensional manifolds}, Author = {Saul, L. K. and Roweis, S. T.}, Journal = {J. Mach. Learn. Res.}, Year = {2003}, Pages = {119--155}, Volume = {4} } @Article{SarTal98, Title = {Orbit spaces of compact coregular simple {Lie} groups with 2, 3 and 4~{b}asic polynomial invariants: {Effective} tools in the analysis of invariant potentials}, Author = {Sartori, G. and Talamini, V.}, Journal = {J. Math. Phys.}, Year = {1998}, Pages = {2367--2401}, Volume = {39}, DOI = {10.1063/1.532294} } @Article{Sartori91, author = {Sartori, G.}, title = {Geometric invariant theory: a model-independent approach to spontaneous symmetry and/or supersymmetry breaking}, journal = {Rivista Nuovo Cim.}, year = {1991}, volume = {14}, pages = {1--120}, doi = {10.1007/BF02810048}, } @Article{SarVal05, Title = {Constructive axiomatic approach to the determination of the orbit spaces of coregular compact linear groups}, Author = {Sartori, G. and Valente, G.}, Journal = {Acta Appl. Math.}, Year = {2005}, Pages = {191--228}, Volume = {87}, DOI = {10.1007/s10440-005-1144-y} } @Article{SarVal05a, Title = {The radial problem in gauge field theory models}, Author = {G. Sartori and G. Valente}, Journal = {Ann. Phys.}, Year = {2005}, Pages = {286--325}, Volume = {319}, DOI = {10.1016/j.aop.2005.04.016} } @Article{SarVal05b, Title = {Tools in the orbit space approach to the study of invariant functions: rational parametrization of strata}, Author = {Sartori, G. and Valente, G.}, Journal = {J. Phys. A}, Year = {2003}, Pages = {1913}, Volume = {36}, DOI = {10.1088/0305-4470/36/7/308} } @Article{SarVal06, Title = {Orbit spaces of reflection groups with 2, 3 and 4~basic polynomial invariants}, Author = {Sartori, G. and Valente, G.}, Journal = {J. Phys. A}, Year = {1996}, Pages = {193}, Volume = {29}, DOI = {10.1088/0305-4470/29/1/019} } @Article{SaScWu97, Title = {Dynamics of spiral waves on unbounded domains using center-manifold reductions}, Author = {Sandstede, B. and Scheel, A. and Wulff, C.}, Journal = {J. Diff. Eqn.}, Year = {1997}, Pages = {122--149}, Volume = {141}, DOI = {10.1006/jdeq.1997.3326} } @Incollection{SaScWu99, author = {Sandstede, B. and Scheel, A. and Wulff, C.}, title = {Dynamical behavior of patterns with {Euclidean} symmetry}, booktitle = {{Pattern Formation in Continuous and Coupled Systems}}, publisher = {Springer}, year = {1999}, pages = {249--264}, address = {New York}, doi = {10.1007/978-1-4612-1558-5_19}, } @Article{SaScWu99a, author = {Sandstede, B. and Scheel, A. and Wulff, C.}, journal = {J. Nonlin. Sci.}, title = {Bifurcations and dynamics of spiral waves}, year = {1999}, pages = {439--478}, volume = {9}, doi = {10.1007/s003329900076}, } @Article{SaStVi12, author = {Sakellariadou, M. and Stabile, A. and Vitiello, G.}, title = {Noncommutative spectral geometry, dissipation and the origin of quantization}, journal = {J. Phys. Conf. Ser.}, year = {2012}, volume = {361}, pages = {012025}, doi = {10.1088/1742-6596/361/1/012025}, } @Book{Satija16, title = {{Butterfly in the Quantum World}}, publisher = {Morgan and Claypool}, year = {2016}, author = {Satija, I. I.}, doi = {10.1088/978-1-6817-4117-8}, isbn = {978-1-6817-4117-8} } @Article{SBM95, Title = {Exactly conservative integrators}, Author = {B. A. Shadwick and J. C. Bowman and P. J. Morrison}, Journal = {SIAM J. Sci. Comput}, Year = {1998}, Pages = {1112--1133}, Volume = {59}, DOI = {10.1137/S0036139995289313} } @Article{SCD07, Title = {On the state space geometry of the {Kuramoto-Sivashinsky} flow in a periodic domain}, Author = {Cvitanovi{\'c}, P. and Davidchack, R. L. and Siminos, E.}, Journal = {SIAM J. Appl. Dyn. Syst.}, Year = {2010}, Pages = {1--33}, Volume = {9}, DOI = {10.1137/070705623} } @Unpublished{SCD09b, Title = {Recurrent spatio-temporal structures of translationally invariant {Kuramoto-Sivashinsky} flow}, Author = {Siminos, E. and Cvitanovi{\'c}, P. and Davidchack, R. L.}, Note = {{In} preparation}, Year = {2010} } @Article{ScFrKa82, author = {M. Schell and S. Fraser and R. Kapral}, title = {Diffusive dynamics in systems with translational symmetry: {A} one--dimensional--map model}, journal = {Phys. Rev. A}, year = {1982}, volume = {26}, pages = {504--521}, doi = {10.1103/PhysRevA.26.504}, } @Article{Schafhaeutl40, Title = {{LXXXVI. On} the combinations of carbon with silicon and iron, and other metals, forming the different species of cast iron, steel, and malleable iron}, Author = {C. Schafhaeutl}, Journal = {Philos. Mag. Ser. 3}, Year = {1840}, Pages = {570--590}, Volume = {16}, DOI = {10.1080/14786444008650094} } @PhdThesis{Scherer91, author = {P. Scherer}, title = {{Quantenzust{\"a}nde eines Klassisch Chaotischen {Billards}}}, school = {Univ. K{\"{o}}ln}, year = {1991}, } @Article{Schiff94, Title = {Controlling chaos in the brain}, Author = {Schiff, S. J. and Jerger, K. and Duong, D. H. and Chang, T. and Spano, M. L. and Ditto, W. L.}, Journal = {Nature}, Year = {1994}, Pages = {615--620}, Volume = {370}, DOI = {10.1038/370615a0} } @Phdthesis{BartschPhD, author = {T. Bartsch}, title = {{The hydrogen atom in an electric field and in crossed electric and magnetic fields: {Closed}-orbit theory and semiclassical quantization}}, school = {Theoretische Physik, U. Stuttgart}, year = {2002}, url = {http://www.itp1.uni-stuttgart.de/publikationen/abschlussarbeiten/bartsch_doktor_2002.pdf}, } @Book{Schouten89, title = {{Tensor Analysis for Physicists}}, publisher = {Dover}, year = {1989}, author = {Schouten, J. A.}, address = {New York}, isbn = {9780486655826}, doi = {10.1063/1.3067367}, } @Book{Schulman, title = {{Techniques and Applications of Path Integration}}, publisher = {Wiley-Interscience}, year = {1981}, author = {Schulman, L. S.}, isbn = {9780486137025}, address = {New York}, doi = {10.1063/1.2914703}, } @Book{Schutz80, author = {Schutz, B. F.}, publisher = {Cambridge Univ. Press}, title = {{Geometrical Methods of Mathematical Physics}}, year = {1980}, address = {Cambridge UK}, doi = {10.1017/cbo9781139171540}, } @Article{Schwartz62, Title = {Global cross sections of compact dynamical systems}, Author = {Schwartzman, S.}, Journal = {Proc. Natl. Acad. Sci. USA}, Year = {1962}, Pages = {786--791}, Volume = {48}, DOI = {10.1073/pnas.48.5.786} } @Article{Schwartz66, author = {J. Schwartz}, journal = {Studies in Logic and the Foundations of Mathematics}, title = {The pernicious influence of mathematics on science}, year = {1966}, pages = {356--360}, volume = {44}, doi = {10.1016/S0049-237X(09)70603-2}, } @Article{Schwartz83, Title = {Estimating regions of existence of unstable periodic orbits using computer-based techniques}, Author = {I. B. Schwartz}, Journal = {SIAM J. Numer. Anal.}, Year = {1983}, Pages = {106--120}, Volume = {20}, DOI = {10.1137/0720008} } @Article{Schwarz79, Title = {Instantons and fermions in the field of instanton}, Author = {Schwarz, A. S.}, Journal = {Commun. Math. Phys.}, Year = {1979}, Pages = {233--268}, Volume = {64}, DOI = {10.1007/BF01221733} } @Misc{Sci.nonlFAQ, Title = {{Sci.nonlinear FAQ, Computational Resources}}, Author = {J. D. Meiss}, Year = {2003}, Institution = {U. Colorado Boulder}, URL = {http://amath.colorado.edu/faculty/jdm/faq.html} } @Article{science04, Title = {Experimental observation of nonlinear traveling waves in turbulent pipe flow}, Author = {B. Hof and C. W. H. van Doorne and J. Westerweel and F. T. M. Nieuwstadt and H. Faisst and B. Eckhardt and H. Wedin and R. R. Kerswell and F. Waleffe}, Journal = {Science}, Year = {2004}, Pages = {1594--1598}, Volume = {305}, DOI = {10.1126/science.1100393} } @Article{SD98, author = {P. Schmelcher and F. K. Diakonos}, title = {General appoach to the localization of unstable periodic orbits in chaotic dynamical systems}, journal = {Phys. Rev. E}, year = {1998}, volume = {57}, pages = {2739}, doi = {10.1103/physreve.57.2739}, } @Article{SE00, author = {A. Schmiegel and B. Eckhardt}, title = {Persistent turbulence in annealed plane {Couette} flow}, journal = {Europhys. Lett.}, year = {2000}, volume = {51}, pages = {395--400}, doi = {10.1209/epl/i2000-00507-2}, } @Article{Seg96, Title = {Book review: {Alain Connes, Noncommutative geometry}}, Author = {I. Segal}, Journal = {Bull. Amer. Math. Soc.}, Year = {1996}, Pages = {459--465}, Volume = {33}, DOI = {10.1090/S0273-0979-96-00687-8} } @Article{Selberg56, author = {Selberg, A.}, title = {Harmonic analysis and discontinuous groups in weakly symmetric {Riemannian} spaces with applications to {Dirichlet} series}, journal = {J. Indian Math. Soc. (N.S.)}, year = {1956}, volume = {20}, pages = {47--87}, } @Book{seydel, title = {{From Equilibrium to Chaos: {Practical} Bifurcation and Stability Analysis}}, publisher = {Elsevier}, year = {1988}, author = {R. Seydel}, isbn = {9780444012500}, address = {New York}, url = {http://euklid.mi.uni-koeln.de/~seydel/buch2.html}, } @Article{Sezgin06, Title = {On the statistical analysis of {Feigenbaum} constants}, Author = {F. Sezgin and T. M. Sezgin}, Journal = {J. Franklin Institute}, Year = {2006}, Pages = {756--758}, Volume = {343}, DOI = {10.1016/j.jfranklin.2006.10.004} } @Book{SH82, title = {{Praktische Mathematik}}, publisher = {Vieweg+Teubner}, year = {1982}, author = {Stummel, F. and Hainer, K.}, isbn = {9783663111214}, doi = {10.1007/978-3-663-11121-4}, } @Article{SH83, Title = {Periodically forced linear oscillator with impacts: {Chaos} and long-period motions}, Author = {S. W. Shaw and P. J. Holmes}, Journal = {Phys. Rev. Lett.}, Year = {1983}, Pages = {623--626}, Volume = {51}, DOI = {10.1103/PhysRevLett.51.623} } @Article{shannon, author = {C. Shannon}, journal = {Bell System Technical Journal}, title = {A mathematical theory of communication}, year = {1948}, pages = {379}, volume = {27}, doi = {10.1002/j.1538-7305.1948.tb00917.x}, } @Article{Shar, Title = {Coexistence of cycles of a continuous map of a line into itself}, Author = {{\v{S}}arkovskii, A. N.}, Journal = {Ukrain. Math. J.}, Year = {1964}, Pages = {61--71}, Volume = {16}, DOI = {10.1142/S0218127495000934} } @Article{SHcgl90, Title = {Pulses and fronts in the complex {Ginzburg-Landau} equation near a subcritical bifurcation}, Author = {van Saarloos, W. and P. C. Hohenberg}, Journal = {Phys. Rev. Lett.}, Year = {1990}, Pages = {749}, Volume = {64}, DOI = {10.1103/PhysRevLett.64.749} } @Article{shch04fli, author = {E. Shchekinova and C. Chandre and Y. Lan and T. Uzer}, title = {Analyzing intramolecular dynamics by fast {Lyapunov} indicators}, journal = {J. Chem. Phys.}, year = {2004}, volume = {121}, pages = {1--7}, doi = {10.1063/1.1756875}, } @Article{SHcoh92, author = {van Saarloos, W. and Hohenberg, P. C.}, title = {Fronts, pulses, sources and sinks in generalized complex {Ginzburg-Landau} equations}, journal = {Physica D}, year = {1992}, volume = {56}, pages = {303--367}, doi = {10.1016/0167-2789(92)90175-m}, } @Article{Shenker82, Title = {Scaling behavior in a map of a circle onto itself:{Empirical} results}, Author = {S. J. Shenker}, Journal = {Physica D}, Year = {1982}, Pages = {405--411}, Volume = {5}, DOI = {10.1016/0167-2789(82)90033-1} } @Article{ShiDol16, Title = {Binary black hole shadows, chaotic scattering and the {Cantor} set}, Author = {J. O. Shipley and S. R. Dolan}, Journal = {Class. Quantum Grav.}, Year = {2016}, Pages = {175001}, Volume = {33}, DOI = {10.1088/0264-9381/33/17/175001} } @Misc{ShoMor15, Title = {Systems and methods for chaotic entanglement using cupolets}, Author = {Short, K. M. and Morena, M. A.}, Note = {US Patent App. 14/370,445}, Year = {2015}, Publisher = {Google Patents}, URL = {https://www.google.com/patents/US20150025658} } @Article{Shraiman81, Title = {Scaling theory for noisy period-doubling transitions to chaos}, Author = {B. Shraiman and C. E. Wayne and P. C. Martin}, Journal = {Phys. Rev. Lett.}, Year = {1981}, Pages = {935--939}, Volume = {46}, DOI = {10.1103/PhysRevLett.46.935} } @Article{shroff1099, author = {G. M. Shroff and H. B. Keller}, title = {Stabilization of unstable procedures: the recursive projection method}, journal = {SIAM J. Numer. Anal.}, year = {1993}, volume = {30}, pages = {1099--1120}, doi = {10.1137/0730057}, } @Article{SiCvi10, Title = {Continuous symmetry reduction and return maps for high-dimensional flows}, Author = {Siminos, E. and Cvitanovi{\'c}, P.}, Journal = {Physica D}, Year = {2011}, Pages = {187--198}, Volume = {240}, DOI = {10.1016/j.physd.2010.07.010} } @Phdthesis{Sieber91, author = {M. Sieber}, title = {{The Hyperbola Billiard: A Model for the Semiclassical Quantization of Chaotic Systems}}, school = {Hamburg Univ.}, year = {1991}, note = {DESY report 91-030}, } @Article{siegel42, author = {C. L. Siegel}, title = {Iteration of analytic functions}, journal = {Ann. Math.}, year = {1942}, volume = {43}, pages = {607--612}, doi = {10.2307/1968952}, } @Article{SieStei90, Title = {Classical and quantum mechanics of a strongly chaotic billiard system}, Author = {Sieber, M. and Steiner, F.}, Journal = {Physica D}, Year = {1990}, Pages = {248--266}, Volume = {44}, DOI = {10.1016/0167-2789(90)90058-W} } @Article{SieStei91, Title = {Quantization of chaos}, Author = {Sieber, M. and Steiner, F.}, Journal = {Phys. Rev. Lett.}, Year = {1991}, Pages = {1941--1944}, Volume = {67}, DOI = {10.1103/PhysRevLett.67.1941} } @Unpublished{siminos11, Title = {Stability of nonlinear {Vlasov} equilibria through spectral deformation and {Fourier-{Hermit}e} expansion}, Author = {Siminos, E. and B{\'e}nisti, D. and Gremillet, L.}, Note = {Submitted}, Year = {2010} } @PhdThesis{SiminosThesis, author = {Siminos, E.}, title = {{Recurrent Spatio-temporal Structures in Presence of Continuous Symmetries}}, school = {School of Physics, Georgia Inst. of Technology}, year = {2009}, address = {Atlanta}, url = {http://ChaosBook.org/projects/theses.html}, } @Article{Simo79, author = {Sim{\'o}, C.}, journal = {J. Stat. Phys.}, title = {On the {H{\'e}non-Pomeau} attractor}, year = {1979}, pages = {465--494}, volume = {21}, doi = {10.1007/BF01009612}, } @InCollection{simo89, author = {C. Sim{\'o}}, title = {On the analytical and numerical approximation of invariant manifolds}, booktitle = {{Les M{\'e}thodes Modernes de la M{\'e}canique C{\'e}leste (Goutelas '89)}}, publisher = {Editions Frontieres}, year = {1989}, editor = {D. Benest and C. Froeschl{\'e}}, pages = {285--329}, address = {Gif-sur-Yvette, France}, isbn = {9782863320914}, } @Article{simon03, Title = {Calculations of periodic orbits for {Hamiltonian} systems with regularizable singularities}, Author = {N. S. Simonovi{\'c}}, Journal = {Few-Body-Systems}, Year = {2003}, Pages = {183--192}, Volume = {32}, DOI = {10.1007/s00601-003-0004-4} } @Article{simon99, Title = {Calculations of periodic orbits: {The} monodromy method and application to regularized systems}, Author = {N. S. Simonovi{\'c}}, Journal = {Chaos}, Year = {1999}, Pages = {854--864}, Volume = {9}, DOI = {10.1063/1.166457} } @Article{sinai, author = {Sinai, Ya. G.}, journal = {Russ. Math. Surv.}, title = {Gibbs measures in ergodic theory}, year = {1972}, pages = {21--69}, volume = {27}, doi = {10.1070/RM1972v027n04ABEH001383}, } @Article{Sinai04, Title = {What is ... a billiard}, Author = {Sinai, Ya. G.}, Journal = {Notices Amer. Math. Soc.}, Year = {2004}, Pages = {412--413}, Volume = {51}, URL = {http://www.ams.org/notices/200404/what-is.pdf} } @Article{Sinai68, Title = {Construction of {Markov} partitions}, Author = {Sinai, Ya. G.}, Journal = {Funct. Anal. Appl.}, Year = {1968}, Pages = {245--253}, Volume = {2}, DOI = {10.1007/BF01076126} } @Article{Sinai70, author = {Sinai, Ya. G.}, title = {Dynamical systems with elastic reflections}, journal = {Russ. Math. Surv.}, year = {1970}, volume = {25}, pages = {137--189}, doi = {10.1070/RM1970v025n02ABEH003794} } @Book{sinai76, author = {Sinai, Ya. G.}, publisher = {Princeton Univ. Press}, title = {{Introduction to Ergodic Theory}}, year = {1976}, address = {Princeton}, isbn = {9780691081823}, } @Article{SinVul80, author = {Sinai, Ya. G. and Vul, E. B.}, title = {Discovery of closed orbits of dynamical systems with the use of computers}, journal = {J. Stat. Phys.}, year = {1980}, volume = {23}, doi = {10.1007/BF01014428}, } @Article{sirovcgl90, author = {J. D. Rodriguez and L. Sirovich}, title = {Low-dimensional dynamics for the complex {Ginzburg-Landau} equation}, journal = {Physica D}, year = {1990}, volume = {43}, pages = {77--86}, doi = {10.1016/0167-2789(90)90017-j}, } @Article{Sirovich94, Title = {Reply to ``{O}bservations regarding '{Coherence} and chaos in a model of turbulent boundary layer' by {X}. {L. Sirovich and X. Zhou}''}, Author = {L. Sirovich and X. Zhou}, Journal = {Phys. Fluids}, Year = {1994}, Pages = {1579--1582}, Volume = {6} } @Article{siv, Title = {Nonlinear analysis of hydrodynamical instability in laminar flames - {I}. {D}erivation of basic equations}, Author = {G. I. Sivashinsky}, Journal = {Acta Astronaut.}, Year = {1977}, Pages = {1177--1206}, Volume = {4}, DOI = {10.1016/0094-5765(77)90096-0} } @Article{sivmich80, Title = {On irregular wavy flow of a liquid down a vertical plane}, Author = {G. I. Sivashinsky and D. M. Michelson}, Journal = {Progr. Theor. Phys. Suppl.}, Year = {1980}, Pages = {2112--2114}, Volume = {66}, DOI = {On irregular wavy flow of a liquid down a vertical plane} } @Article{SK05, Title = {Localization of periodic orbits of polynomial systems by ellipsoidal estimates}, Author = {K. E. Starkov and A. P. Krishchenko}, Journal = {Chaos Solit. Fract.}, Year = {2005}, Pages = {981--988}, Volume = {23}, DOI = {10.1016/j.chaos.2004.06.002} } @Article{ShenKad82, author = {Shenker, S. J. and Kadanoff, L. P.}, title = {Critical behavior of a {KAM} surface: {I}. {Empirical} results}, journal = {J. Stat. Phys.}, year = {1982}, volume = {27}, pages = {631--656}, doi = {10.1007/BF01013439}, } @Article{Skokos02, Title = {Alignment indices: a new, simple method for determining the ordered or chaotic nature of orbits}, Author = {Skokos, C.}, Journal = {J. Phys. A}, Year = {2001}, Pages = {10029--10043}, Volume = {34}, DOI = {10.1088/0305-4470/34/47/309} } @Incollection{Skokos08, author = {Skokos, Ch.}, title = {The {Lyapunov} characteristic exponents and their computation}, booktitle = {{Dynamics of Small Solar System Bodies and Exoplanets}}, publisher = {Springer}, year = {2010}, editor = {Souchay, J. J. and Dvorak, R.}, isbn = {978-3-642-04457-1}, pages = {63--135}, address = {New York}, doi = {10.1007/978-3-642-04458-8_2}, } @Article{skowr07, author = {L. Skowronek and P. F. Gora}, title = {Chaos in {Newtonian} iterations: {Searching} for zeros which are not there}, journal = {Acta Phys. Polonica B}, year = {2007}, volume = {38}, pages = {1909}, url = {http://www.actaphys.uj.edu.pl/fulltext?series=Reg&vol=38&page=1909}, } @Article{Sma05, Title = {On the hyperbolicity of the period-doubling fixed point}, Author = {D. Smania}, Journal = {Trans. Amer. Math. Soc.}, Year = {2006}, Pages = {1827--1846}, Volume = {358}, DOI = {10.1090/S0002-9947-05-03803-1} } @Article{smale, Title = {Differentiable dynamical systems}, Author = {S. Smale}, Journal = {Bull. Amer. Math. Soc.}, Year = {1967}, Pages = {747--817}, Volume = {73}, DOI = {10.1090/S0002-9904-1967-11798-1} } @Article{smale_61, Title = {Generalized {Poincar{\'e}}'s conjecture in dimensions greater than four}, Author = {S. Smale}, Journal = {Ann. Math.}, Year = {1961}, Pages = {199--406}, Volume = {74}, DOI = {10.2307/1970239} } @Book{Smale00, title = {{The Collected Papers of {Stephen Smale}}}, publisher = {World Scientific}, year = {2000}, author = {S. Smale and F. Cucker and R. Wong}, isbn = {978-981-02-4307-4}, address = {Singapore}, doi = {10.1142/4424-vol1}, } @Article{Smale70I, Title = {Topology and mechanics, {I}.}, Author = {S. Smale}, Journal = {Inv. Math.}, Year = {1970}, Pages = {305--331}, Volume = {10}, DOI = {10.1007/BF01418778} } @Article{Smale70II, Title = {Topology and mechanics, {II}.}, Author = {S. Smale}, Journal = {Inv. Math.}, Year = {1970}, Pages = {45--64}, Volume = {11}, DOI = {10.1007/BF01389805} } @Book{Smale80, title = {{The Mathematics of Time}}, publisher = {Springer}, year = {1980}, author = {S. Smale}, isbn = {9781461381013}, address = {New York}, doi = {10.1007/978-1-4613-8101-3}, } @Article{SMcgl02, author = {J. Scheuer and B. A. Malomed}, title = {Stable and chaotic solutions of the complex {Ginzburg-Landau} equation with periodic boundary conditions}, journal = {Physica D}, year = {2002}, volume = {161}, pages = {102--115}, doi = {10.1016/s0167-2789(01)00363-3}, } @Article{Smithies41, author = {Smithies, F.}, title = {The {Fredholm} theory of integral equations}, journal = {Duke Math. J.}, year = {1941}, volume = {8}, pages = {107--130}, doi = {10.1215/S0012-7094-41-00805-0}, } @Article{SOGY92, Title = {Using chaos to direct orbits to targets in systems describable by a one-dimensional map}, Author = {Shinbrot, TT. and C. Grebogi and E. Ott and J. A. Yorke}, Journal = {Phys. Rev. A}, Year = {1992}, Pages = {4165--4168}, Volume = {45}, DOI = {10.1103/PhysRevA.45.4165} } @Article{solomon1994chaotic, Title = {Chaotic advection in a two-dimensional flow: {L{\'e}vy} flights and anomalous diffusion}, Author = {Solomon, T. H. and Weeks, E. R. and Swinney, H. L.}, Journal = {Physica D}, Year = {1994}, Pages = {70--84}, Volume = {76}, DOI = {10.1016/0167-2789(94)90251-8} } @Book{SoNaMi96, author = {Solari, H. G. and Natiello, M. A. and Mindlin, G. B.}, publisher = {Taylor \& Francis}, title = {{Nonlinear Dynamics: A Two-Way Trip from Physics to Math}}, year = {1996}, doi = {10.1201/9780203745618}, } @Book{Sontag98, author = {Sontag, E. D.}, publisher = {Springer}, title = {{Mathematical Control Theory: Deterministic Finite Dimensional Systems}}, year = {1998}, address = {New York}, doi = {10.1007/978-1-4612-0577-7}, } @Book{Sou97, title = {{Structure of Dynamical Systems}}, publisher = {Birkh\"auser}, year = {1997}, author = {J.-M. Souriau}, address = {Boston}, doi = {10.1007/978-1-4612-0281-3}, } @Article{Spalart91, author = {P. R. Spalart and R. D. Moser and M. M. Rogers}, journal = {J. Comp. Phys.}, title = {Spectral methods for the {Navier-Stokes} equations with one infinite and two periodic directions}, year = {1990}, pages = {297--324}, volume = {96}, doi = {10.1016/0021-9991(91)90238-g}, } @Article{spald91, author = {D. B. Spalding}, title = {Kolmogorov's two-equation model of turbulence}, journal = {Proc. R. Soc. Lond. A}, year = {1991}, volume = {434}, pages = {211--216}, doi = {10.1098/rspa.1991.0089}, } @Book{sparrow, title = {{The {Lorenz} Equations: {Bifurcations}, Chaos and Strange Attractors}}, publisher = {Springer}, year = {1982}, author = {C. Sparrow}, address = {New York}, doi = {10.1007/978-1-4612-5767-7}, } @Article{spercgl, author = {W. Sch{\"{o}}pf and L. Kramer}, title = {Small-amplitude periodic and chaotic solutions of the complex {Ginzburg-Landau} equation for a subcritical bifurcation}, journal = {Phys. Rev. Lett.}, year = {1991}, volume = {66}, pages = {2316}, doi = {10.1103/physrevlett.66.2316}, } @Book{spfunc1, title = {{Special Functions: An Introduction to the Classical Functions of Mathematical Physics}}, publisher = {Wiley}, year = {1996}, author = {N. M. Temme}, address = {New York}, doi = {10.1002/9781118032572}, } @Misc{SpiekerBlog, Title = {Gone fishin' - a blog}, Author = {W. Spieker}, HowPublished = {School of Physics, Georgia Inst. of Technology, (Atlanta, )}, Year = {2011}, URL = {http://ChaosBook.org/projects/Spieker} } @Book{sprott03, title = {{Chaos and Time-series Analysis}}, publisher = {Oxford Univ. Press}, year = {2003}, author = {Sprott, J. C.}, isbn = {9780198508403}, address = {Oxford}, } @Article{Spruill07, author = {Spruill, M. C.}, title = {Asymptotic distribution of coordinates on high dimensional spheres}, journal = {Elect. Comm. in Probab.}, year = {2007}, volume = {12}, pages = {234--247}, doi = {10.1214/ecp.v12-1294}, } @Article{SPScgl92, author = {B. I. Shraiman and A. Pumir and van Saarloos, W. and Hohenberg, P. C. and H. Chat{\'e} and M. Holen}, title = {Spatiotemporal chaos in the one-dimensional complex {Ginzburg-Landau} equation}, journal = {Physica D}, year = {1992}, volume = {57}, pages = {241--248}, doi = {10.1016/0167-2789(92)90001-4}, } @InProceedings{SreeVanDoo93, author = {Sreedhar, J. and Van Dooren, P.}, booktitle = {{Proc. 1993 Conf. Information Sciences \& Systems, {Johns Hopkins Univ.}}}, title = {Discrete-time periodic systems: a {Floquet} approach}, year = {1993}, url = {https://www.researchgate.net/publication/2258958_Discrete-Time_Periodic_Systems_A_Floquet_Approach}, } @InProceedings{SreeVanDoo93a, author = {Sreedhar, J. and Van Dooren, P.}, title = {Pole placement via the periodic {Schur} decomposition}, booktitle = {{American Control Conference}}, year = {1993}, pages = {1563--1567}, doi = {10.23919/ACC.1993.4793135}, } @InProceedings{SreeVanDoo93b, author = {Sreedhar, J. and Van Dooren, P.}, booktitle = {{Proc. 32. IEEE Conference on Decision and Control}}, title = {Solution of periodic discrete-time {Riccati} and {Lyapunov} equations}, year = {1993}, pages = {361--362}, volume = {1}, doi = {10.1109/CDC.1993.325128}, } @Article{SrViWi95, author = {Srivastava, Y. N. and Vitiello, G. and Widom, A.}, journal = {Ann. Phys. (N.Y.)}, title = {Quantum dissipation and quantum noise}, year = {1995}, pages = {200--207}, volume = {238}, doi = {10.1006/aphy.1995.1019}, } @Article{SS97, Title = {Chaotic family with smooth {Lyapunov} dependence}, Author = {Stoop, R. and Steeb, W. H.}, Journal = {Phys. Rev. E}, Year = {1997}, Pages = {7763--7766}, Volume = {55}, DOI = {10.1103/PhysRevE.55.7763} } @Inbook{S-S97, chapter = {Geometric integration}, pages = {121--143}, title = {{The State of the Art in Numerical Analysis}}, publisher = {Clarendon Press}, year = {1997}, author = {J. M. Sanz-Serna}, editor = {I. S. Duff and G. A. Watson}, address = {Oxford UK}, } @Article{SSL10, author = {G. S{\'a}nchez-Arriaga and E. Siminos and E. Lefebvre}, journal = {submitted}, title = {Solitary waves with nonvanishing boundary conditions in relativistic plasmas}, year = {2010}, url = {http://cns.gatech.edu/~siminos/papers/SSL10.pdf}, } @Article{stabpcgl, author = {B. J. Matkowsky and V. Volpert}, title = {Stability of plane wave solutions of complex {Ginzburg-Landau} equations}, journal = {Quart. Appl. Math.}, year = {1993}, volume = {51}, pages = {265--281}, url = {http://www.jstor.org/stable/43637924}, } @Unpublished{stadium95, author = {Hansen, K. T. and Cvitanovi{\'c}, P.}, note = {{\em J. Stat. Phys.}, accepted 1996, revised version still not resubmitted}, title = {Symbolic dynamics and {Markov} partitions for the stadium billiard}, year = {1995}, eprint = {chao-dyn/9502005}, eprintclass = {chao-dyn}, eprinttype = {arxiv}, } @Article{StaSte11, Title = {Asymptotic estimates and stability analysis of {Kuramoto-Sivashinsky} type models}, Author = {M. Stanislavova and A. Stefanov}, Journal = {J. Evol. Eqs.}, Year = {2011}, Pages = {605--635}, Volume = {11}, DOI = {10.1007/s00028-011-0103-5} } @Article{SteDuMei04, author = {H. R. Dullin and J. D. Meiss and D. G. Sterling}, title = {Symbolic codes for rotational orbits}, journal = {SIAM J. Appl. Dyn. Sys.}, year = {2005}, volume = {4}, pages = {515--562}, doi = {10.1137/040612877}, } @Article{SteDuMei99, author = {Sterling, D. G. and Dullin, H. R. and Meiss, J. D.}, journal = {Physica D}, title = {Homoclinic bifurcations for the {H{\'e}non} map}, year = {1999}, pages = {153--184}, volume = {134}, doi = {10.1016/S0167-2789(99)00125-6}, } @Article{Steeb83, author = {Steeb, W. H.}, title = {Embedding of nonlinear finite dimensional systems in linear infinite dimensional systems and {Bose} operators}, journal = {Hadronic J.}, year = {1983}, volume = {6}, pages = {68--76}, } @Article{steiner, Title = {Quantum chaos in the hyperbola billiard}, Author = {M. Sieber and F. Steiner}, Journal = {Phys. Lett. A}, Year = {1990}, Pages = {415--420}, Volume = {148}, DOI = {10.1016/0375-9601(90)90492-7} } @Article{sten94sol, author = {L. Stenflo and O. M. Gradov}, title = {Solitary surface-wave deformation of a plasma boundary}, journal = {Phys. Plasmas}, year = {1994}, volume = {1}, pages = {2804}, doi = {10.1063/1.870516}, } @Article{sten98osc, author = {L. Stenflo and M. Y. Yu}, title = {Plasma oscillons in spherically bounded magnetized plasmas}, journal = {Phys. Plasmas}, year = {1998}, volume = {5}, pages = {3122}, doi = {10.1063/1.873038}, } @Article{Stephen1991, Title = {Formulae for cycles in the {Mandelbrot} set}, Author = {Stephenson, J.}, Journal = {Physica A}, Year = {1991}, Pages = {416--420}, Volume = {190}, DOI = {10.1016/0378-4371(91)90181-B} } @Article{Stephen1992A, Title = {Formulae for cycles in the {Mandelbrot} set {II}}, Author = {Stephenson, J. and Ridgway, D. T.}, Journal = {Physica A}, Year = {1992}, Pages = {104--116}, Volume = {190}, DOI = {10.1016/0378-4371(92)90080-A} } @Article{Stephen1992B, Title = {Formulae for cycles in the {Mandelbrot} set {III}}, Author = {Stephenson, J.}, Journal = {Physica A}, Year = {1992}, Pages = {117--129}, Volume = {190}, DOI = {10.1016/0378-4371(92)90081-Z} } @Article{sternb57, Title = {Local contractions and a theorem of {Poincar\'e}}, Author = {S. Sternberg}, Journal = {Amer. J. Math.}, Year = {1957}, Pages = {809--824}, Volume = {79}, DOI = {10.2307/2372437} } @Article{sternb58, Title = {On the structure of local homeomorphisms of {Euclidean} n-space, {II}}, Author = {S. Sternberg}, Journal = {Amer. J. Math.}, Year = {1958}, Pages = {623--631}, Volume = {80}, DOI = {10.2307/2372774} } @Article{sternb59, Title = {The structure of local homeomorphisms}, Author = {S. Sternberg}, Journal = {Amer. J. Math.}, Year = {1959}, Pages = {578}, Volume = {81}, DOI = {10.2307/2372915} } @Unpublished{stevenj, Title = {Topics in applied mathematics}, Author = {Johnson, S. G.}, Note = {MIT course 18.325}, Year = {2005}, URL = {http://math.mit.edu/~stevenj/18.325/representation-theory.pdf} } @Book{StGo09, author = {Stone, M. and Goldbart, P.}, publisher = {Cambridge Univ. Press}, title = {{Mathematics for Physics: A Guided Tour for Graduate Students}}, year = {2009}, address = {Cambridge UK}, doi = {10.1017/cbo9780511627040}, } @Article{StMeiss98, Title = {Computing periodic orbits using the anti-integrable limit}, Author = {D. Sterling and J. D. Meiss}, Journal = {Phys. Lett. A}, Year = {1998}, Pages = {46--52}, Volume = {241}, DOI = {10.1016/S0375-9601(98)00094-2} } @Book{Stockmann07, author = {H.-J. St{\"{o}}ckmann}, publisher = {Cambridge Univ. Press}, title = {{Quantum Chaos: An Introduction}}, year = {2007}, address = {Cambridge UK}, isbn = {9780521027151}, } @Article{Stokes1847, Title = {On the numerical calculation of a class of definite integrals and infinite series}, Author = {G. G. Stokes}, Journal = {Trans. Camb. Phil. Soc.}, Year = {1851}, Pages = {166--187}, Volume = {9}, URL = {https://archive.org/stream/transactionsofca09camb#page/n181/mode/2up} } @Article{Stokes1864, Title = {On the discontinuity of arbitrary constants which appear in divergent developments}, Author = {G. G. Stokes}, Journal = {Trans. Camb. Phil. Soc.}, Year = {1864}, Pages = {166--187}, Volume = {10}, URL = {https://archive.org/stream/transactionsofca09camb#page/n181/mode/2up} } @Article{Stone05, author = {Stone, D.}, title = {Einstein's unknown insight and the problem of quantizing chaos}, journal = {Phys. Today}, year = {2005}, volume = {58}, pages = {37--43}, doi = {10.1063/1.2062917}, } @Book{Str88, title = {{Linear Algebra and Its Applications}}, publisher = {Academic}, year = {1988}, author = {G. Strang}, isbn = {9780155510050}, address = {New York}, } @Book{Stratonovich, title = {{Conditional {Markov} Processes and Their Application to the Theory of Control}}, publisher = {Elsevier}, year = {1968}, author = {R. L. Stratonovich}, address = {New York}, } @Mastersthesis{Strepparava95, Author = {R. Strepparava}, School = {Universit{\'a} degli Studi di Milano}, Year = {1995}, Note = {Laurea thesis} } @Book{strogb, author = {S. H. Strogatz}, publisher = {Westview Press}, title = {{Nonlinear Dynamics and Chaos}}, year = {2014}, address = {Boulder, CO}, doi = {10.1201/9780429492563}, } @Article{StrWan02, Title = {Instability of traveling waves of the {Kuramoto-Sivashinsky} equation}, Author = {Strauss, W. and Wang, G.}, Journal = {Chin. Ann. Math.}, Year = {2002}, Pages = {267--276}, Volume = {23}, DOI = {10.1142/S0252959902000250}, } @Article{SumRules, author = {Cvitanovi{\'c}, P. and Hansen, Kim and Rolf, J. and Vattay, G.}, title = {Beyond the periodic orbit theory}, journal = {Nonlinearity}, year = {1998}, volume = {11}, pages = {1209--1232}, doi = {10.1088/0951-7715/11/5/003}, } @InProceedings{sunil_ahuja_template-based_2006, Title = {Template-based stabilization of relative equilibria}, Author = {S. Ahuja and {I.G.} Kevrekidis and {C.W.} Rowley}, Booktitle = {{2006 American Control Conference, 14-16 June 2006}}, Year = {2006}, Address = {Piscataway, NJ}, Pages = {3606--3611}, Publisher = {{IEEE}}, DOI = {10.1109/ACC.2006.1657278} } @Article{SunKanZha11, Title = {A method of recovering the initial vectors of globally coupled map lattices based on symbolic dynamics}, Author = {Sun, L.-S. and Kang, X.-Y. and Zhang, Q. and Lin, L.-X.}, Journal = {Chin. Phys. B}, Year = {2011}, Pages = {120507}, Volume = {20}, DOI = {10.1088/1674-1056/20/12/120507} } @Article{SWG02, author = {P. A. Stone and F. Waleffe and M. D. Graham}, title = {Toward a structural understanding of turbulent drag reduction: nonlinear coherent states in viscoelastic shear flows}, journal = {Phys. Rev. Lett.}, year = {2002}, volume = {89}, pages = {20831}, doi = {10.1103/physrevlett.89.208301}, } @Article{SwiDy02, author = {H. P. F. Swinnerton-Dyer}, title = {The invariant algebraic surfaces of the {Lorenz} system}, journal = {Math. Proc. Cambridge Philos. Soc.}, year = {2002}, volume = {132}, pages = {385}, doi = {10.1017/s0305004101005667}, } @Article{SwiWie84, author = {Swift, J. W. and Wiesenfeld, K.}, title = {Suppression of period doubling in symmetric systems}, journal = {Phys. Rev. Lett.}, year = {1984}, volume = {52}, pages = {705--708}, doi = {10.1103/PhysRevLett.52.705} } @InCollection{symb_dyn, author = {P. Cvitanovi\'{c}}, title = {Charting the state space}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2020}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/paper.shtml#knead}, } @Article{symmcgl, author = {A. Doelman}, title = {Breaking the hidden symmetry in the {Ginzburg-Landau} equation}, journal = {Physica D}, year = {1996}, volume = {97}, pages = {398--428}, doi = {10.1016/0167-2789(95)00303-7}, } @Article{szendro-20072, Title = {Spatiotemporal structure of {Lyapunov} vectors in chaotic coupled-map lattices}, Author = {I. G. Szendro and D. Paz\'o and M. A. Rodr\'{i}guez and J. M. L\'opez}, Journal = {Phys. Rev. E}, Year = {2007}, Pages = {025202}, Volume = {76}, DOI = {10.1103/PhysRevE.76.025202} } @Book{Tabor89, title = {{Chaos and Integrability in Nonlinear Dynamics: An Introduction}}, publisher = {Wiley}, year = {1989}, author = {M. Tabor}, isbn = {978-0-471-82728-3}, address = {New York}, doi = {10.5860/choice.27-2142}, } @Misc{TaCe09, author = {Takenouchi, Y. and Celeste, R.}, title = {Representation of period doubling by digraphs and characteristic polynomials}, year = {2009}, eprint = {0909.0335}, eprinttype = {arxiv}, } @Article{TaCh12, author = {Takeuchi, K. A. and Chat\'e, H.}, journal = {J. Phys. A}, title = {Collective {Lyapunov} modes}, year = {2013}, pages = {254007}, volume = {46}, doi = {10.1088/1751-8113/46/25/254007}, } @Article{Tadi05, Title = {On computing periodic orbits}, Author = {M. Tadi}, Journal = {J. Sound Vib.}, Year = {2005}, Pages = {495--506}, Volume = {283}, DOI = {10.1016/j.jsv.2004.06.011} } @Article{TaGiCh09, Title = {{Lyapunov} analysis captures the collective dynamics of large chaotic systems}, Author = {Takeuchi, K. A. and Ginelli, F. and Chat{\'e}, H.}, Journal = {Phys. Rev. Lett.}, Year = {2009}, Pages = {154103}, Volume = {103}, DOI = {10.1103/PhysRevLett.103.154103} } @Article{TaGiCh11, Title = {Hyperbolic decoupling of tangent space and effective dimension of dissipative systems}, Author = {Takeuchi, K. A. and Yang, {H.-l.} and Ginelli, F. and Radons, G. and Chat\'{e}, H.}, Journal = {Phys. Rev. E}, Year = {2011}, Pages = {046214}, Volume = {84}, DOI = {10.1103/PhysRevE.84.046214} } @Article{tajima02, author = {S. Tajima and H. S. Greenside}, title = {Microextensive chaos of a spatially extended system}, journal = {Phys. Rev. E}, year = {2002}, volume = {66}, pages = {017205}, doi = {10.1103/physreve.66.017205}, } @Article{Takada01, author = {Takada, H. and Kitaoka, Y. and Shimizua, Y.}, journal = {Forma}, title = {Mathematical index and model in stabirometry}, year = {2001}, pages = {17--46}, volume = {16}, url = {http://ci.nii.ac.jp/naid/10006657190/en/}, } @Incollection{Takens81, author = {Takens, F.}, title = {Detecting strange attractors in turbulence}, booktitle = {{Dynamical Systems and Turbulence}}, publisher = {Springer}, year = {1981}, editor = {Rand, D. A. and Young, L.-S.}, isbn = {978-3-540-11171-9}, pages = {366--381}, address = {New York}, doi = {10.1007/bfb0091924}, } @Article{TakOon84, author = {Takahashi, Y. and Oono, Y.}, title = {Towards the statistical mechanics of chaos}, journal = {Progr. Theor. Phys}, year = {1984}, volume = {71}, pages = {851--854}, doi = {10.1143/PTP.71.851}, } @Misc{TaoBlog, author = {T. Tao}, title = {{What's New}}, year = {2010}, url = {http://terrytao.wordpress.com/}, } @Article{TaSa07, Title = {Role of unstable periodic orbits in phase transitions of coupled map lattices}, Author = {Takeuchi, K. and Sano, M.}, Journal = {Phys. Rev. E}, Year = {2007}, Pages = {036201}, Volume = {75}, DOI = {10.1103/PhysRevE.75.036201} } @Article{TaWi92, Title = {Quantization of chaotic systems}, Author = {G. Tanner and D. Wintgen}, Journal = {Chaos}, Year = {1992}, Pages = {53}, Volume = {2}, DOI = {10.1063/1.165897} } @Article{tbohr, author = {M. Bazhenov and T. Bohr and K. Gorshkov and M. Rabinovich}, title = {The diversity of steady state solutions of the complex {Ginzburg-Landau} equation}, journal = {Phys. Lett. A}, year = {1996}, volume = {217}, pages = {104}, doi = {10.1016/0375-9601(96)00328-3}, } @Article{tdisk, Title = {Fractal properties of scattering singularities}, Author = {B. Eckhardt}, Journal = {J. Phys. A}, Year = {1987}, Pages = {5971--5979}, Volume = {20}, DOI = {10.1088/0305-4470/20/17/030} } @Article{Tel89, author = {T{\'e}l, T.}, title = {On the organisation of transient chaos-application to irregular scattering}, journal = {J. Phys. A}, year = {1989}, volume = {22}, pages = {L691--L698}, doi = {10.1088/0305-4470/22/14/008}, } @Book{TelGr06, author = {T{\'e}l, T. and Gruiz, M.}, publisher = {Cambridge Univ. Press}, title = {{Chaotic Dynamics: An Introduction Based on Classical Mechanics}}, year = {2006}, address = {Cambridge UK}, doi = {10.1017/cbo9780511803277}, } @Article{temam91edd, author = {R. T{\'e}mam}, title = {Approximation of attractors, large eddy simulations and multiscale methods}, journal = {Proc. R. Soc. Lond. A}, year = {1991}, volume = {434}, pages = {23--39}, doi = {10.1098/rspa.1991.0078}, } @Article{Terrac06, author = {Terracini, S.}, title = {On the variational approach to the periodic {$N$}-body problem}, journal = {Celestial Mech. Dynam. Astronom.}, year = {2006}, volume = {95}, pages = {3--25}, doi = {10.1007/s10569-006-9025-x}, } @Book{terras, title = {{Harmonic Analysis on Symmetric Spaces and Applications {I}}}, publisher = {Springer}, year = {1985}, author = {A. Terras}, isbn = {9780387961590}, address = {Berlin}, doi = {10.1007/978-1-4612-5128-6}, } @Book{Terras10, author = {Terras, A.}, publisher = {Cambridge Univ. Press}, title = {{Zeta Functions of Graphs: A Stroll through the Garden}}, year = {2010}, address = {Cambridge UK}, doi = {10.1017/cbo9780511760426}, } @Article{Teytel99, Title = {How rare are multiple eigenvalues?}, Author = {Teytel, M.}, Journal = {Commun. Pure Appl. Math.}, Year = {1999}, Pages = {917--934}, Volume = {52}, DOI = {10.1002/(SICI)1097-0312(199908)52:8<917::AID-CPA1>3.0.CO;2-S} } @Article{TF08, Title = {Rigorous numerical approximation of {Ruelle-Perron-Frobenius} operators and topological pressure of expanding maps}, Author = {D. Terhesiu and G. Froyland}, Journal = {Nonlinearity}, Year = {2008}, Pages = {1953}, Volume = {21}, DOI = {10.1088/0951-7715/21/9/001} } @Article{TFGphase97, Title = {Studies of phase turbulence in the one dimensional complex {Ginzburg-Landau} equation}, Author = {A. Torcini and H. Frauenkron and P. Grassberger}, Journal = {Phys. Rev. E}, Year = {1997}, Pages = {5073}, Volume = {55}, DOI = {10.1103/PhysRevE.55.5073} } @Book{Thirring79, title = {{Quantum Mechanics of Atoms and Molecules}}, publisher = {Springer}, year = {1979}, author = {W. Thirring}, volume = {3}, isbn = {9783709175231}, address = {New York}, note = {Page 48, Sects. 2.3.21 and 2.3.22 .}, } @Article{Thi02, author = {Thiffeault, J.-L.}, journal = {Physica D}, title = {Derivatives and constraints in chaotic flows: asymptotic behaviour and a numerical method}, year = {2002}, pages = {139--161}, volume = {172}, doi = {10.1016/S0167-2789(02)00588-2}, } @Article{ThiBoo99, author = {Thiffeault, {J.-L.} and Boozer, A. H.}, title = {Geometrical constraints on finite-time {Lyapunov} exponents in two and three dimensions}, journal = {Chaos}, year = {2001}, volume = {11}, pages = {16--28}, doi = {10.1063/1.1342079}, } @Article{Thom1, Title = {Chaos after period-doubling bifurcations in the resonance of an impact oscillator}, Author = {J. M. T. Thompson and R. Ghaffari}, Journal = {Phys. Lett. A}, Year = {1982}, Pages = {5--8}, Volume = {91}, DOI = {10.1016/0375-9601(82)90248-1} } @Article{Thom2, Title = {Subharmonic and chaotic motions of compliant offshore structures and articulated mooring towers}, Author = {J. M. T. Thompson and A. R. Bokaian and R. Ghaffari}, Journal = {J. Energy Resour. Technol. (Trans ASME)}, Year = {1984}, Pages = {191--198}, Volume = {106}, DOI = {10.1115/1.3231037} } @Inproceedings{tHooft00, author = {{'t Hooft}, G.}, title = {Determinism and dissipation in quantum gravity}, booktitle = {{Basics and Highlights in Fundamental Physics}}, year = {2001}, pages = {397--413}, publisher = {World Scientific Pub Co Pte Lt}, doi = {10.1142/9789812811585_0015}, } @Article{tHooft01a, Title = {Determinism in free bosons}, Author = {{'t Hooft}, G.}, Journal = {Int. J. Theor. Phys.}, Year = {2003}, Pages = {355--361}, Volume = {42}, DOI = {10.1023/A:1024459703072} } @InProceedings{tHooft01b, author = {{'t Hooft}, G.}, booktitle = {{8th International Symposium on Particles Strings and Cosmology (PASCOS 2001) Chapel Hill, North Carolina, April 2001}}, title = {Quantum mechanics and determinism}, year = {2001}, eprint = {hep-th/0105105}, eprintclass = {hep-th}, eprinttype = {arxiv}, } @Article{tHooft07, Title = {A mathematical theory for deterministic quantum mechanics}, Author = {{'t Hooft}, G.}, Journal = {J. Phys.: Conf. Series}, Year = {2007}, Pages = {012015}, Volume = {67}, DOI = {10.1088/1742-6596/67/1/012015} } @Article{tHooft99, Title = {Quantum gravity as a dissipative deterministic system}, Author = {{'t Hooft}, G.}, Journal = {Classical and Quantum Gravity}, Year = {1999}, Pages = {3263--3279}, Volume = {16}, DOI = {10.1088/0264-9381/16/10/316} } @InCollection{tHooftVelt73, author = {{'t Hooft}, G. and Veltman, M.}, booktitle = {{Particle Interactions at Very High Energies}}, publisher = {Springer}, title = {{DIAGRAMMAR}}, year = {1974}, address = {Berlin}, pages = {177--322}, doi = {10.1007/978-1-4684-2826-1_5}, } @Book{ThoSte02, title = {{Nonlinear Dynamics and Chaos: Geometrical Methods for Engineers and Scientists}}, publisher = {Wiley}, year = {2002}, author = {J. M. T. Thompson and H. B. Stewart}, isbn = {978-0-471-87645-8}, address = {New York}, } @PhdThesis{Thum05, author = {V. Th\"ummler}, title = {{Numerical Analysis of the Method of Freezing Traveling Waves}}, school = {Bielefeld Univ.}, year = {2005}, url = {https://pub.uni-bielefeld.de/publication/2306350}, } @Article{Thurston88, Title = {On the geometry and dynamics of diffeomorphisms of surfaces}, Author = {Thurston, W. P.}, Journal = {Bull. Amer. Math. Soc.}, Year = {1988}, Pages = {417--431}, Volume = {19}, URL = {http://projecteuclid.org/euclid.bams/1183554722} } @Article{TiCo01, author = {M. K. Tippett and S. E. Cohn}, journal = {Nonlin. Proc. Geophys.}, title = {Adjoints and low-rank covariance representation}, year = {2001}, pages = {331--340}, volume = {8}, url = {https://hal.archives-ouvertes.fr/hal-00302042}, } @Book{Tinkham, title = {{Group Theory and Quantum Mechanics}}, publisher = {Dover}, year = {2003}, author = {Tinkham, M.}, isbn = {9780486131665}, address = {New York}, doi = {10.1016/c2013-0-01646-5}, } @Article{T-NK02, Title = {Statistical-mechanical formulation of {Lyapunov} exponents}, Author = {S. Tanase-Nicola and J. Kurchan}, Journal = {J. Phys. A}, Year = {2003}, Pages = {10299}, Volume = {36}, DOI = {10.1088/0305-4470/36/41/004} } @Article{ToDe94, Title = {Geometric phases in lasers and liquid flows}, Author = {Toronov, V. Y. and Derbov, V. L.}, Journal = {Phys. Rev. E}, Year = {1994}, Pages = {1392--1399}, Volume = {49}, DOI = {10.1103/PhysRevA.49.1392} } @Article{ToDe94a, Title = {Geometric-phase effects in laser dynamics}, Author = {Vladislav Yu. Toronov and Vladimir L. Derbov}, Journal = {Phys. Rev. A}, Year = {1994}, Pages = {878--881}, Volume = {50}, DOI = {10.1103/PhysRevA.50.878} } @Article{ToDe97a, author = {Toronov, V. Y. and Derbov, V. L.}, title = {Boundedness of attractors in the complex {Lorenz} model}, journal = {Phys. Rev. E}, year = {1997}, volume = {55}, pages = {3689--3692}, doi = {10.1103/physreve.55.3689}, } @Article{ToDe98, author = {Toronov, V. Y. and Derbov, V. L.}, title = {Topological properties of laser phase}, journal = {J. Optical Soc. of America B}, year = {1998}, volume = {15}, pages = {1282--1290}, doi = {10.1364/josab.15.001282}, } @Article{Tomlinson29, Title = {{CVI}. {A} molecular theory of friction}, Author = {G. A. Tomlinson}, Journal = {Philos. Mag. Ser. 7}, Year = {1929}, Pages = {905--939}, Volume = {7}, DOI = {10.1080/14786440608564819} } @Article{tompaid96, Title = {Numerical study of invariant sets of a quasi-periodic perturbation of a symplectic map}, Author = {S. Tompaidis}, Journal = {Experiment. Math.}, Year = {1996}, Pages = {211--230}, Volume = {5}, DOI = {10.1080/10586458.1996.10504589} } @Article{tompaid96a, author = {S. Tompaidis}, journal = {Experiment. Math.}, title = {Approximation of invariant surfaces by periodic orbits in high-dimensional maps: {Some} rigorous results}, year = {1996}, pages = {197--209}, volume = {5}, doi = {10.1080/10586458.1996.10504588}, } @Article{torc96, author = {A. Torcini}, title = {Order parameter for the transition from phase to amplitude turbulence}, journal = {Phys. Rev. Lett.}, year = {1996}, volume = {77}, pages = {1047}, doi = {10.1103/physrevlett.77.1047}, } @Article{toricgl, author = {P. Tak\'{a}\v{c}}, title = {Invariant 2-tori in the time-dependent {Ginzburg-Landau} equation}, journal = {Nonlinearity}, year = {1992}, volume = {5}, pages = {289--321}, doi = {10.1088/0951-7715/5/2/002}, } @InCollection{torino, author = {P. Cvitanovi{\'c}}, booktitle = {{Noise and Chaos in Nonlinear Dynamical Systems}}, publisher = {Cambridge Univ. Press}, title = {Chaos for cyclists}, year = {1989}, address = {Cambridge UK}, editor = {E. Moss and L. A. Lugiato and W. Schleich}, isbn = {9780521384179}, url = {http://ChaosBook.org/~predrag/papers/preprints.html#torino}, } @Book{Townsend76, author = {A. A. Townsend}, publisher = {Cambridge U. Press}, title = {{The Structure of Turbulent Shear Flows}}, year = {1976}, address = {Cambridge}, edition = {2}, } @Article{transgol, author = {Ramshankar, R. and Gollub, J. P.}, journal = {Phys. Fluids A}, title = {Transport by capillary waves, part {II}: {Scalar} dispersion and the structure of the concentration field}, year = {1991}, pages = {1344}, volume = {3}, } @Book{Trefethen97, title = {{Numerical Linear Algebra}}, publisher = {SIAM}, year = {1997}, author = {L. N. Trefethen and D. Bau}, addr = {Philadelphia}, doi = {10.1137/1.9780898719574}, } @Article{TrePan98, author = {Trevisan, A. and Pancotti, F.}, journal = {J. Atmos. Sci.}, pages = {390}, title = {Periodic orbits, {Lyapunov} vectors, and singular vectors in the {Lorenz} system}, volume = {55}, year = {1998}, doi = {10.1175/1520-0469(1998)055<0390:polvas>2.0.co;2}, } @Article{TrIsTa09, Title = {Four-dimensional variational assimilation in the unstable subspace and the optimal subspace dimension}, Author = {A. Trevisan and M. D'Isidoro and O. Talagrand}, Journal = {Quart. J. Roy. Meteorol. Soc.}, Year = {2010}, Pages = {487--496}, Volume = {136}, DOI = {10.1002/qj.571} } @Article{Troll91, Title = {A devil's staircase into chaotic scattering}, Author = {G. Troll}, Journal = {Physica D}, Year = {1991}, Pages = {276--296}, Volume = {50}, DOI = {10.1016/0167-2789(91)90180-H} } @Book{Truesdell91, Title = {{A First Course in Rational Continuum Mechanics. General Concepts}}, Author = {Truesdell, C. A.}, Publisher = {Academic}, Year = {1977}, Address = {New York}, ISBN = {978-0-12-701300-8}, Volume = {1} } @Article{TS86, Title = {New approach to the problem of chaotic repellers}, Author = {Sz\'epfalusy, P. and T\'el, T.}, Journal = {Phys. Rev. A}, Year = {1986}, Pages = {2520--2523}, Volume = {34}, DOI = {10.1103/PhysRevA.34.2520} } @Article{TsKuYa94, Title = {Thermal effects and dissipation in {su(1, 1)}-algebraic model by means of time-dependent variational approach}, Author = {Tsue, Y. and Kuriyama, A. and Yamamura, M.}, Journal = {Progr. Theor. Phys.}, Year = {1994}, Pages = {469--494}, Volume = {91}, DOI = {10.1143/ptp/91.3.469} } @Article{TTRD93, author = {Trefethen, L. N. and Trefethen, A. E. and Reddy, S. C. and Driscoll, T. A.}, journal = {Science}, title = {Hydrodynamic stability without eigenvalues}, year = {1993}, pages = {578--584}, volume = {261}, doi = {10.1126/science.261.5121.578}, } @Article{TuckBar03, author = {L. S. Tuckerman and D. Barkley}, title = {Symmetry breaking and turbulence in perturbed plane {Couette} flow}, journal = {Theor. Comp. Fluid Dyn.}, year = {2002}, volume = {16}, pages = {91--97}, doi = {10.1007/s00162-002-0064-y}, } @Article{tucker1, author = {W. Tucker}, title = {The {Lorenz} attractor exists}, journal = {C. R. Acad. Sci. Paris S{\'e}r. I Math.}, year = {1999}, volume = {328}, pages = {1197--1202}, doi = {10.1016/s0764-4442(99)80439-x}, } @Article{tucker2, author = {Tucker, W.}, title = {A rigorous {ODE} solver and {Smale}'s 14th problem}, journal = {Found. Comp. Math.}, year = {2002}, volume = {2}, pages = {53--117}, doi = {10.1007/s002080010018}, } @Book{tuf91, title = {{An Experimental Approach to Nonlinear Dynamics and Chaos}}, publisher = {Addison-Wesley}, year = {1992}, author = {Tufillaro, N. and Abbott, T. and Reilly, J.}, isbn = {9780201554410}, address = {Redwood City}, doi = {10.1119/1.17380}, } @Book{Tung85, title = {{Group Theory in Physics}}, publisher = {World Scientific}, year = {1985}, author = {Tung, W.-K.}, isbn = {978-9971-966-57-7}, address = {Singapore}, doi = {10.1142/0097}, } @Article{Uezu00, Title = {Superconvergence of period doubling cascade in trapezoid maps: {Its} rigorous proof and superconvergence of the period-doubling cascade starting from a period p solution}, Author = {Uezu, T.}, Journal = {Progr. Theor. Phys.}, Year = {2000}, Pages = {23--53}, Volume = {104}, DOI = {10.1143/PTP.104.23} } @InCollection{UFOlund, author = {Cvitanovi{\'c}, P.}, booktitle = {{Order and Chaos in Non-linear Physical System}}, publisher = {Plenum}, title = {Renormalization description of transitions to chaos}, year = {1988}, address = {New York}, editor = {S. Lundquist, N. H. March and Tosi, M. P.}, isbn = {9781489920584}, pages = {73--97}, doi = {10.1007/978-1-4899-2058-4_12}, } @Article{UH, Title = {Decay of the velocity autocorrelation function for the periodic {Lorentz} gas}, Author = {Friedman, B. and Martin Jr., R. F.}, Journal = {Phys. Lett. A}, Year = {1984}, Pages = {23--26}, Volume = {105}, DOI = {10.1016/0375-9601(84)90554-1} } @Book{Ulam60, title = {{A Collection of Mathematical Problems}}, publisher = {Interscience}, year = {1960}, author = {Ulam, S. M.}, address = {New York}, } @Article{umb94pat, author = {F. Melo and P. Umbanhowar and H. L. Swinney}, title = {Transition to parametric wave patterns in a vertically oscillated granular layer}, journal = {Phys. Rev. Lett.}, year = {1994}, volume = {72}, pages = {172--175}, doi = {10.1103/physrevlett.72.172}, } @Article{UruKoc90, Title = {New metric elements of the universal fine structure due to multifurcations}, Author = {V. Urumov and L. Kocarev}, Journal = {Phys. Lett. A}, Year = {1990}, Pages = {220}, Volume = {144}, DOI = {10.1016/0375-9601(90)90924-D} } @Article{Valance, Title = {Dynamics of a ball bouncing on a rough inclined line}, Author = {A. Valance and D. Bideau}, Journal = {Phys. Rev. E}, Year = {1998}, Pages = {1886}, Volume = {57}, DOI = {10.1103/PhysRevE.57.1886} } @Article{Vance92, Title = {Unstable periodic-orbits and transport-properties of nonequilibrium steady-states}, Author = {W. N. Vance}, Journal = {Phys. Rev. Lett.}, Year = {1992}, Pages = {1356--1359}, Volume = {69}, DOI = {10.1103/PhysRevLett.69.1356} } @Misc{Vanderb, author = {Vanderbauwhede, A.}, title = {On the continuation of relative periodic orbits in reversible systems}, url = {http://cage.ugent.be/~avdb/english/publications.htm}, } @Article{vanderbauwhede_example_2000, author = {Vanderbauwhede, A.}, title = {An example of symmetry reduction in {Hamiltonian} systems}, journal = {Int. Conf. on Differential Equations, Berlin, Germany, 1-7 August 1999}, year = {2000}, doi = {10.1142/9789812792617_0043}, } @Book{vanderbauwhede_heteroclinic_1992, title = {{Heteroclinic Cycles and Periodic Orbits in Reversible Systems}}, publisher = {Pitman}, year = {1992}, author = {Vanderbauwhede, A.}, address = {Boston}, pages = {250}, } @Book{vanderbauwhede_local_1982, title = {{Local Bifurcation and Symmetry}}, publisher = {Pitman}, year = {1982}, author = {Vanderbauwhede, A.}, address = {Boston}, } @Phdthesis{vanderbauwhede_lokale_1980, Title = {{Lokale Bifurcatietheorie en Symmetrie}}, Author = {Vanderbauwhede, A.}, School = {Rijksuniv. Gent, Fac. van de Wetenschappen}, Year = {1980} } @InCollection{vanderbauwhede_normal_1995, author = {Vanderbauwhede, A.}, booktitle = {{Dynamical Systems and Applications}}, publisher = {World Scientific}, title = {Normal forms and versal unfoldings of symplectic linear mappings}, year = {1995}, pages = {685--700}, volume = {4}, doi = {10.1142/9789812796417_0045}, } @Unpublished{vanderbauwhede_short_1997, Title = {A short tutorial on {Hamiltonian} systems and their reduction near a periodic orbit}, Author = {Vanderbauwhede, A.}, Year = {1997} } @Article{vanderbauwhede_topics_1994, author = {Vanderbauwhede, A.}, journal = {SIAM Rev.}, title = {{Topics in Bifurcation Theory and Applications} {(Gerard Iooss and Moritz Adelmeyer)}}, year = {1994}, pages = {323}, volume = {36}, doi = {10.1137/1036090}, } @Inproceedings{Vanderbauwhede1989, author = {A. Vanderbauwhede}, title = {Centre manifolds, normal forms and elementary bifurcations}, booktitle = {{Dynamics Reported}}, year = {1989}, editor = {U. Kirchgraber and H. O. Walther}, volume = {4}, pages = {89--169}, address = {New York}, publisher = {Wiley}, doi = {10.1007/978-3-322-96657-5_4}, } @Article{VanDooSree94, Title = {When is a periodic discrete-time system equivalent to a time-invariant one?}, Author = {Van Dooren, P. and Sreedhar, J.}, Journal = {Linear Algebra Appl.}, Year = {1994}, Pages = {131--151}, Volume = {212-213}, DOI = {10.1016/0024-3795(94)90400-6} } @Article{VanHove54, Title = {Correlations in space and time and {Born} approximation scattering in systems of interacting particles}, Author = {Van Hove, L.}, Journal = {Phys. Rev.}, Year = {1954}, Pages = {249--262}, Volume = {95}, DOI = {10.1103/PhysRev.95.249} } @Article{varcyc, Title = {{Newton} method for highly unstable orbits}, Author = {B. D. Mestel and I. Percival}, Journal = {Physica D}, Year = {1987}, Pages = {172}, Volume = {24}, DOI = {10.1016/0167-2789(87)90072-8} } @InProceedings{Varga01, Title = {On balancing and order reduction of unstable periodic systems}, Author = {Varga, A.}, Booktitle = {Periodic Control Systems 2001}, Year = {2001}, Address = {New York}, Editor = {S. Bittanti and P. Colaneri}, Organization = {IFAC Workshop}, Pages = {177--182}, Publisher = {Elsevier}, ISBN = {978-0-08-043682-1}, URL = {http://elib.dlr.de/22687/1/varga_como01p2.pdf} } @InProceedings{Varga05, author = {Varga, A.}, booktitle = {{Proc. IFAC Workshop on Periodic Control Systems}}, title = {A periodic systems toolbox for {MATLAB}}, year = {2005}, pages = {474--474}, volume = {16}, doi = {10.3182/20050703-6-cz-1902.00475}, } @InProceedings{Varga11, author = {Varga, A.}, booktitle = {{Proc. IFAC Workshop on Periodic Control Systems}}, title = {An overview of recent developments in computational methods for periodic systems}, year = {2011}, doi = {10.3182/20070829-3-ru-4912.00027}, } @Article{Varga97, Title = {Periodic {Lyapunov} equations: {Some} applications and new algorithms}, Author = {Varga, A.}, Journal = {Int. J. Control}, Year = {1997}, Pages = {69--88}, Volume = {67}, DOI = {10.1080/002071797224360} } @InProceedings{VarVanD01, Title = {Computational methods for periodic systems-an overview}, Author = {Varga, A. and Van Dooren, P.}, Booktitle = {Periodic Control Systems 2001}, Year = {2001}, Address = {New York}, Editor = {S. Bittanti and P. Colaneri}, Organization = {IFAC Workshop}, Pages = {171--176}, Publisher = {Elsevier}, ISBN = {978-0-08-043682-1}, URL = {http://elib.dlr.de/11743/1/varga_como01p1.pdf} } @Article{VC08, author = {Viswanath, D. and Cvitanovi{\'c}, P.}, title = {Stable manifolds and the transition to turbulence in pipe flow}, journal = {J. Fluid Mech.}, year = {2009}, volume = {627}, pages = {215--233}, doi = {10.1017/S0022112009006041}, } @Book{VCCPV14, title = {{Large Deviations in Physics}}, publisher = {Springer}, year = {2014}, author = {Vulpiani, A. and Cecconi, F. and Cencini, M. and Puglisi, A. and Vergni, D.}, address = {New York}, doi = {10.1007/978-3-642-54251-0}, pages = {263--293}, } @Article{vdHvB95, Title = {Dynamics on the {SU(2)} fundamental domain}, Author = {van den Heuvel, B. and van Baal, P.}, Journal = {Nucl. Phys. Proc. Suppl.}, Year = {1995}, Pages = {823--825}, Volume = {42}, DOI = {10.1016/0920-5632(95)00392-M} } @Article{VenZog83, author = {Venkov, A. B. and Zograf, P. G.}, journal = {Math. USSR}, title = {On analogues of the {Artin} factorization formulas in the spectral theory of automorphic functions connected with induced representations of {Fuchsian} groups}, year = {1983}, pages = {435--443}, volume = {21}, doi = {10.1070/im1983v021n03abeh001800}, } @Book{Viana97, title = {{Stochastic Dynamics of Deterministic Systems}}, publisher = {IMPA}, year = {1997}, author = {Viana, M.}, volume = {21}, url = {http://w3.impa.br/~viana/out/sdds.pdf}, } @Article{Vierkandt1892, author = {Vierkandt, A.}, journal = {Monatsh. Math. Phys.}, title = {{{\"U}}ber {Gleitende} und {Rollende} {Bewegung}}, year = {1892}, pages = {31--54}, volume = {III}, doi = {10.1007/bf01692422}, } @Article{Visw07b, Title = {Recurrent motions within plane {Couette} turbulence}, Author = {D. Viswanath}, Journal = {J. Fluid Mech.}, Year = {2007}, Pages = {339--358}, Volume = {580}, DOI = {10.1017/S0022112007005459} } @Article{Visw08, author = {D. Viswanath}, title = {The critical layer in pipe flow at high {Reynolds} number}, journal = {Phil. Trans. Royal Soc. A}, year = {2009}, volume = {367}, pages = {561--576}, doi = {10.1098/rsta.2008.0225}, } @Incollection{Viv-1, author = {Baladi, V.}, title = {A brief introduction to dynamical zeta functions}, booktitle = {{Classical Nonintegrability, Quantum Chaos}}, publisher = {Springer}, year = {1997}, editor = {A. Knauf and Ya. G. Sinai}, pages = {3--20}, doi = {10.1007/978-3-0348-8932-2_2}, } @Article{VK79, Title = {Eigenvalues of a diffusion process with a critical point}, Author = {H. Dekker and N. G. Van Kampen}, Journal = {Phys. Lett. A}, Year = {1979}, Pages = {374--376}, Volume = {73}, DOI = {10.1016/0375-9601(79)90088-4} } @Book{vKampen92, author = {van Kampen, N. G.}, publisher = {Elsevier}, title = {{Stochastic Processes in Physics and Chemistry}}, year = {2007}, address = {Amsterdam}, edition = {3}, doi = {10.1016/B978-0-444-52965-7.X5000-4}, } @Article{VKK05, author = {L. van Veen and S. Kida and G. Kawahara}, title = {Periodic motion representing isotropic turbulence}, journal = {Fluid Dyn. Res.}, year = {2006}, volume = {38}, pages = {19--46}, doi = {10.1016/j.fluiddyn.2005.09.001}, } @Article{VlToDe98, Title = {The complex {Lorenz} model: {Geometric} structure, homoclinic bifurcation and one-dimensional map}, Author = {Vladimirov, A. G. and Toronov, V. Y. and Derbov, V. L.}, Journal = {Int. J. Bifur. Chaos}, Year = {1998}, Pages = {723--729}, Volume = {8}, DOI = {10.1142/S0218127498000516} } @Article{VlToDe98a, author = {Vladimirov, A. G. and Toronov, V. Y. and Derbov, V. L.}, title = {Properties of the phase space and bifurcations in the complex {Lorenz} model}, journal = {Technical Physics}, year = {1998}, volume = {43}, pages = {877--884}, doi = {10.1134/1.1259094}, } @Article{vonNeum32, author = {J. von Neumann}, title = {{Zus{\"a}tze zur Arbeit ``Zur Operatorenmethode in der klassischen Mechanik''}. ({German}) [{Additions} to the work ``{On} operator methods in classical mechanics'']}, journal = {Ann. Math.}, year = {1932}, volume = {33}, pages = {789--791}, doi = {10.2307/1968225}, } @Article{Vor92, author = {A. Voros}, journal = {Adv. Studies in Pure Math., Math. Soc. Japan}, title = {Zeta functions in geometry}, year = {1992}, pages = {327--358}, volume = {21}, url = {http://ipht.cea.fr/Docspht/articles/t90/168/public/txt.pdf}, } @Article{Voros87, Title = {Spectral functions, special functions and the {Selberg} zeta function}, Author = {Voros, A.}, Journal = {Commun. Math. Phys.}, Year = {1987}, Pages = {439--465}, Volume = {110}, DOI = {10.1007/BF01212422} } @Article{voth02, author = {G. A. Voth and G. Haller and J. P. Gollub}, title = {Experimental measurements of streching fields in fluid mixing}, journal = {Phys. Rev. Lett.}, year = {2002}, volume = {88}, pages = {254501}, doi = {10.1103/physrevlett.88.254501}, } @Article{vp98, author = {A. Varga and S. Pieters}, title = {Gradient-based approach to solve optimal periodic output feedback control problems}, journal = {Automatica}, year = {1998}, volume = {34}, pages = {477--481}, doi = {10.1016/s0005-1098(97)00214-8}, } @Article{Vrah95, author = {M. N. Vrahatis}, title = {An efficient method for locating and computing periodic orbits of nonlinear mappings}, journal = {J. Comp. Phys.}, year = {1995}, volume = {119}, pages = {105--119}, doi = {10.1006/jcph.1995.1119} } @Article{VTB97, Title = {Equivalence of irreversible entropy production in driven systems: {An} elementary chaotic map approach}, Author = {Vollmer, J\"urgen and T\'el, Tam\'as and Breymann, Wolfgang}, Journal = {Phys. Rev. Lett.}, Year = {1997}, Pages = {2759--2762}, Volume = {79}, DOI = {10.1103/PhysRevLett.79.2759} } @Article{VulKha82, author = {E. B. Vul and K. M. Khanin}, title = {The unstable separatrix of {Feigenbaum}'s fixed-point}, journal = {Russ. Math. Surv.}, year = {1982}, volume = {37}, pages = {200--201}, doi = {10.1070/RM1982v037n05ABEH004046} } @Article{VuSiKh84, author = {Vul, E. B. and Sinai, Ya. G. and Khanin, K. M.}, journal = {Russ. Math. Surv.}, title = {Feigenbaum universality and the thermodynamic formalism}, year = {1984}, pages = {1--40S}, volume = {39}, doi = {10.1070/RM1984v039n03ABEH003162}, } @Article{VWR94, Title = {Periodic orbit theory of diffraction}, Author = {G. Vattay and A. Wirzba and P. E. Rosenqvist}, Journal = {Phys. Rev. Lett.}, Year = {1994}, Pages = {2304--2307}, Volume = {73}, DOI = {10.1103/PhysRevLett.73.2304} } @Article{W01, author = {F. Waleffe}, title = {Exact coherent structures in channel flow}, journal = {J. Fluid Mech.}, year = {2001}, volume = {435}, pages = {93--102}, doi = {10.1017/s0022112001004189}, } @Inproceedings{W02, author = {F. Waleffe}, title = {Exact coherent structures and their instabilities: Toward a dynamical-system theory of shear turbulence}, booktitle = {{Dynamics and Statistics of Coherent Structures in Turbulence: Roles of Elementary Vortices'}}, year = {2002}, editor = {Shigeo Kida}, pages = {115--128}, publisher = {National Center of Sciences, Tokyo, Japan}, } @Article{W03, Title = {Homotopy of exact coherent structures in plane shear flows}, Author = {F. Waleffe}, Journal = {Phys. Fluids}, Year = {2003}, Pages = {1517--1543}, Volume = {15}, DOI = {10.1063/1.1566753} } @Article{W90, Title = {A system of one dimensional balls with gravity}, Author = {M. P. Wojtkowski}, Journal = {Commun. Math. Phys.}, Year = {1990}, Pages = {507--533}, Volume = {126}, DOI = {10.1007/BF02125698} } @Article{W90a, Title = {A system of one dimensional balls in an external field. {II}}, Author = {M. P. Wojtkowski}, Journal = {Commun. Math. Phys.}, Year = {1990}, Pages = {425--432}, Volume = {127}, DOI = {10.1007/BF02096765} } @InProceedings{W90b, Title = {On the origin of the streak spacing in turbulent shear flow}, Author = {F. Waleffe}, Booktitle = {Annual Research Briefs}, Year = {1990}, Pages = {159--168}, Publisher = {Center for Turbulence Research, Stanford Univ.} } @Article{W95a, author = {F. Waleffe}, journal = {Stud. Appl. Math.}, title = {Hydrodynamic stability and turbulence: {Beyond} transients to a {Self-Sustaining Process}}, year = {1995}, pages = {319--343}, volume = {95}, doi = {10.1002/sapm1995953319}, } @Article{W95b, Title = {Transition in shear flows: Nonlinear normality versus non-normal linearity}, Author = {F. Waleffe}, Journal = {Phys. Fluids}, Year = {1995}, Pages = {3060--3066}, Volume = {7}, DOI = {10.1063/1.868682} } @Article{W97, Title = {On a {Self-Sustaining Process} in shear flows}, Author = {F. Waleffe}, Journal = {Phys. Fluids}, Year = {1997}, Pages = {883--900}, Volume = {9}, DOI = {10.1063/1.869185} } @Article{W98, author = {F. Waleffe}, title = {Three-dimensional coherent states in plane shear flows}, journal = {Phys. Rev. Lett.}, year = {1998}, volume = {81}, pages = {4140--4148}, doi = {10.1103/physrevlett.81.4140}, } @Article{WaHu, Title = {Anomalous diffusion in dynamical systems: {Transport} coefficients of all order}, Author = {X.-J. Wang and C.-K. Hu}, Journal = {Phys. Rev. E}, Year = {1993}, Pages = {728--733}, Volume = {48}, DOI = {10.1103/PhysRevE.48.728} } @Unpublished{Waleffe90, author = {F. Waleffe}, note = {{Center for Turbulence Research, Stanford Univ./NASA Ames, unpublished preprint (1990)}}, title = {Proposal for a {Self-Sustaining Process} in shear flows}, year = {1990}, url = {http://www.math.wisc.edu/~waleffe/ECS/sspctr90.pdf}, } @Article{Wallace47, author = {Wallace, P. R.}, journal = {Phys. Rev.}, title = {The band theory of graphite}, year = {1947}, pages = {622--634}, volume = {71}, doi = {10.1103/PhysRev.71.622}, } @InCollection{WalPant97, author = {F. Waleffe and J. Kim}, booktitle = {{Self-Sustaining Mechanisms} of Wall Bounded Turbulence}, publisher = {Computational Mechanics Publications}, title = {How streamwise rolls and streaks self-sustain in a shear flow}, year = {1997}, address = {Southampton}, editor = {R. L. Panton}, pages = {385--422}, url = {http://www.math.wisc.edu/~waleffe/ECS/WK97.pdf}, } @Book{Walt82, title = {{An Introduction to Ergodic Theory}}, publisher = {Springer}, year = {1981}, author = {P. Walters}, isbn = {9780387951522}, address = {New York}, doi = {10.1007/978-1-4612-5775-2}, } @Article{Wang89a, Title = {Abnormal fluctuations and thermodynamic phase transitions in dynamical systems}, Author = {Wang, X.-J.}, Journal = {Phys. Rev. A}, Year = {1989}, Pages = {3214--3217}, Volume = {39}, DOI = {10.1103/PhysRevA.39.3214} } @Article{Wang89b, Title = {Statistical physics of temporal intermittency}, Author = {Wang, X.-J.}, Journal = {Phys. Rev. A}, Year = {1989}, Pages = {6647--6661}, Volume = {40}, DOI = {10.1103/PhysRevA.40.6647} } @Book{Wat07, title = {{The Matrix Eigenvalue Problem: GR and Krylov Subspace Methods}}, publisher = {SIAM}, year = {2007}, author = {Watkins, D. S.}, address = {Philadelphia}, doi = {10.1137/1.9780898717808}, } @Book{Wat10, author = {Watkins, D. S.}, publisher = {Wiley}, title = {{Fundamentals of Matrix Computations}}, year = {2010}, address = {New York}, edition = {3}, isbn = {978-0-470-52833-4}, doi = {10.1002/0471249718}, } @Book{Wax, title = {{Selected Papers on Noise and Stochastic Processes}}, publisher = {Dover}, year = {1954}, author = {E. N. Wax}, isbn = {9780486495354}, address = {New York}, doi = {10.1063/1.3062012}, } @Article{WeBaKuPoSch14, Title = {Formation and interaction of resonance chains in the open three-disk system}, Author = {T. Weich and S. Barkhofen and U. Kuhl and C. Poli and H. Schomerus}, Journal = {New J. Phys.}, Year = {2014}, Pages = {033029}, Volume = {16}, DOI = {10.1088/1367-2630/16/3/033029} } @Phdthesis{Weich14, Title = {{Singular Equivariant Spectral Asymptotics of Schr{\"o}dinger Operators in R\^{} n and Resonances of {Schottky} Surfaces}}, Author = {Weich, T.}, School = {Philipps-Universit{\"a}t Marburg}, Year = {2014} } @Article{Weil49, Title = {Numbers of solutions of equations in finite fields}, Author = {Weil, A.}, Journal = {Bull. Amer. Math. Soc}, Year = {1949}, Pages = {497--508}, Volume = {55}, DOI = {10.1090/S0002-9904-1949-09219-4} } @Book{Weinberg1972, title = {{Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity}}, publisher = {Wiley}, year = {1972}, author = {Weinberg, S.}, isbn = {9780471925675}, address = {New York}, doi = {10.1119/1.1987308}, } @Article{weiss82, author = {J. Weiss and M. Tabor and G. Carnevale}, title = {The {Painlev{\'e}} property for partial differential equations}, journal = {J. Math. Phys.}, year = {1983}, volume = {24}, pages = {522}, doi = {10.1063/1.525721}, } @Article{weiss83, author = {Weiss, J.}, journal = {J. Math. Phys.}, title = {The {Painlev{\'e}} for partial differential equations.{II}: {B\"{a}cklund} transformation, {Lax} pairs, and the {Schwarzian} derivative}, year = {1983}, pages = {1405}, volume = {24}, doi = {10.1063/1.525875}, } @Article{weiss86, author = {J. Weiss}, title = {{B\"{a}cklund} transformation and the {Painlev{\'e}} property}, journal = {J. Math. Phys.}, year = {1986}, volume = {27}, pages = {1293}, doi = {10.1063/1.527134}, } @Misc{WeissFeig, Title = {Feigenbaum constant}, Author = {Weisstein, E. W.}, Year = {2012}, Publisher = {Wolfram MathWorld}, URL = {http://mathworld.wolfram.com/FeigenbaumConstant.html} } @Article{WeOv94, author = {Wells, A. L. J. and Overill, R. E.}, title = {The extension of the {Feigenbaum-Cvitanovi{\'c}} function to the complex plane}, journal = {Int. J. Bifur. Chaos}, year = {1994}, volume = {4}, pages = {1041--1051}, doi = {10.1142/s0218127494000757}, } @Misc{Westbury10, author = {Westbury, B. W.}, title = {Recoupling theory for quantum spinors}, year = {2010}, eprint = {1007.2579}, eprinttype = {arxiv}, } @Book{Weyl31, Title = {{The Theory of Groups and Quantum Mechanics}}, Author = {Weyl, H.}, Publisher = {Dover}, Year = {1931}, Address = {New York}, ISBN = {9780486602691} } @Book{Weyl39, title = {{The Classical Groups: Their Invariants and Representations}}, publisher = {Princeton Univ. Press}, year = {1939}, author = {Weyl, H.}, isbn = {9780691057569}, address = {Princeton, NJ}, doi = {10.1515/9781400883905}, } @Article{WFSBC15, author = {Budanur, N. B. and Short, K. Y. and Farazmand, M. and Willis, A. P. and Cvitanovi{\'c}, P.}, title = {Relative periodic orbits form the backbone of turbulent pipe flow}, journal = {J. Fluid Mech.}, year = {2017}, volume = {833}, pages = {274--301}, doi = {10.1017/jfm.2017.699}, } @Article{Whelan90, Title = {Two balls in one dimension with gravity}, Author = {N. D. Whelan and D. A. Goodings and J. K. Cannizzo}, Journal = {Phys. Rev. A}, Year = {1990}, Pages = {742--754}, Volume = {42}, DOI = {10.1103/PhysRevA.42.742} } @Book{Whitt37, author = {E. T. Whittaker}, publisher = {Cambridge Univ. Press}, title = {{A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: With an Introduction to the Problem of Three Bodies}}, year = {1937}, address = {Cambridge UK}, doi = {10.1017/cbo9780511608797}, } @Article{Widom, author = {M. Widom}, title = {Renormalization group analysis of quasi-periodicity in analytic maps}, journal = {Commun. Math. Phys.}, year = {1993}, volume = {92}, pages = {121}, doi = {10.1007/bf01206316}, } @Book{wiggb, title = {{Global Bifurcations and Chaos}}, publisher = {Springer}, year = {1988}, author = {S. Wiggins}, address = {New York}, doi = {10.1007/978-1-4612-1042-9}, } @Book{wiggins1992, title = {{Chaotic Transport in Dynamical Systems}}, publisher = {Springer}, year = {1992}, author = {S. Wiggins}, address = {N.Y.}, doi = {10.1007/978-1-4757-3896-4}, } @Book{Wigner59, Title = {{Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra}}, Author = {Wigner, E. P.}, Publisher = {Academic}, Year = {1931}, Address = {New York}, ISBN = {9780323152785} } @Misc{wikiHamMat, author = {{Wikipedia contributors}}, title = {Hamiltonian matrix --- {Wikipedia, The Free Encyclopedia}}, year = {2020}, url = {https://en.wikipedia.org/wiki/Hamiltonian_matrix}, } @Article{wikiHoSheBra, author = {P. Holmes and E. T. Shea-Brown}, title = {Stability}, journal = {Scholarpedia}, year = {2006}, volume = {1}, pages = {1838}, doi = {10.4249/scholarpedia.1838}, } @Misc{wikiRossMap, author = {{Wikipedia contributors}}, title = {R{\"o}ssler attractor --- {Wikipedia, The Free Encyclopedia}}, year = {2020}, url = {https://en.wikipedia.org/wiki/Rossler_map}, } @Misc{wikiRouthHurwitzs, author = {{Wikipedia contributors}}, title = {{Routh-Hurwitz} stability criterion --- {Wikipedia, The Free Encyclopedia}}, year = {2020}, url = {https://en.wikipedia.org/wiki/Routh-Hurwitz_stability_criterion}, } @Article{Wilczak03, Title = {Chaos in the {Kuramoto--Sivashinsky} equations---a computer-assisted proof}, Author = {D. Wilczak}, Journal = {J. Diff. Eqn.}, Year = {2003}, Pages = {433--459}, Volume = {194}, DOI = {10.1016/S0022-0396(03)00104-9} } @Misc{Wilson17, author = {L. Wilson}, title = {{Fractals in Chemical Reactions}}, year = {2017}, note = {Undergraduate project, {Loughborough Univ.}}, } @Incollection{Wilkinson09, Title = {Smooth ergodic theory}, Author = {Wilkinson, A.}, Booktitle = {{Encyclopedia of Complexity and Systems Science}}, Publisher = {Springer}, Year = {2009}, Address = {New York}, Editor = {Meyers, R. A.}, Pages = {8168--8183}, DOI = {10.1007/978-0-387-30440-3_484}, ISBN = {978-0-387-75888-6}, URL = {http://www.math.uchicago.edu/~wilkinso/papers/smoothergodictheory.pdf} } @Article{Williams67, author = {Williams, R. F.}, journal = {Topology}, title = {One-dimensional non-wandering sets}, year = {1967}, pages = {473 --487}, volume = {6}, doi = {10.1016/0040-9383(67)90005-5}, } @Inproceedings{Williams70, author = {Williams, R. F.}, title = {Zeta function in global analysis}, booktitle = {{Global Analysis (Proc. Sympos. Pure Math. XIV, Berkeley, CA, 1968)}}, year = {1970}, pages = {335--339}, address = {Providence, RI}, publisher = {Amer. Math. Soc.}, doi = {10.1090/pspum/014/0266252}, } @Book{Wimberger14, title = {{Nonlinear Dynamics and Quantum Chaos}}, publisher = {Springer}, year = {2014}, author = {Wimberger, S.}, address = {New York}, doi = {10.1007/978-3-319-06343-0}, } @Book{Winfree1980, title = {{The Geometry of Biological Time}}, publisher = {Springer}, year = {1980}, author = {A. T. Winfree}, address = {New York}, doi = {10.1007/978-1-4757-3484-3}, } @Article{Winfree73, Title = {Scroll-shaped waves of chemical activity in 3 dimensions}, Author = {A. T. Winfree}, Journal = {Science}, Year = {1973}, Pages = {937--939}, Volume = {181}, DOI = {10.1126/science.181.4103.937} } @Article{Winfree91, author = {A. T. Winfree}, title = {Varieties of spiral wave behavior: {An} experimentalist's approach to the theory of excitable media}, journal = {Chaos}, year = {1991}, volume = {1}, pages = {303--334}, doi = {10.1063/1.165844}, } @Article{Wirzba99, Title = {Quantum mechanics and semiclassics of hyperbolic n-disk scattering systems}, Author = {A. Wirzba}, Journal = {Phys. Rep.}, Year = {1999}, Pages = {1--116}, Volume = {309}, DOI = {10.1016/S0370-1573(98)00036-2} } @Unpublished{wirzbaCasTalk, author = {A. Wirzba}, title = {A force from nothing into nothing: {Casimir} interactions}, note = {Overheads}, year = {2003}, url = {http://ChaosBook/projects/Wirzba/openfull.ps.gz}, } @Article{WiShCv15, Title = {Symmetry reduction in high dimensions, illustrated in a turbulent pipe}, Author = {Willis, A. P. and Short, K. Y. and Cvitanovi{\'c}, P.}, Journal = {Phys. Rev. E}, Year = {2016}, Pages = {022204}, Volume = {93}, DOI = {10.1103/PhysRevE.93.022204} } @Article{witt99hol, author = {R. W. Wittenberg and P. Holmes}, title = {Scale and space localization in the {Kuramoto-Sivashinsky} equation}, journal = {Chaos}, year = {1999}, volume = {9}, pages = {452}, doi = {10.1063/1.166419} } @Article{WiVeBeBo04, author = {D. A. Wisniacki and E. Vergini and R. M. Benito and F. Borondo}, title = {Classical invariants and the quantization of chaotic systems}, journal = {Phys. Rev. E}, year = {2004}, volume = {70}, pages = {035202}, doi = {10.1103/physreve.70.035202}, } @Article{WK04, Title = {Exact coherent structures in pipe flow}, Author = {H. Wedin and R. R. Kerswell}, Journal = {J. Fluid Mech.}, Year = {2004}, Pages = {333--371}, Volume = {508}, DOI = {10.1017/S0022112004009346} } @Inproceedings{WKH93, author = {F. Waleffe and J. Kim and J. Hamilton}, title = {On the origin of streaks in turbulent shear flows}, booktitle = {{Turbulent Shear Flows 8: Eighth International Symposium on Turbulent Shear Flows, Munich}}, year = {1993}, editor = {F. Durst and R. Friedrich and B. E. Launder and F. W. Schmidt and U. Schumann and J. H. Whitelaw}, pages = {37--49}, address = {New York}, publisher = {Springer}, doi = {10.1007/978-3-642-77674-8_4}, } @Article{Wolfram1984, Title = {Computation theory of cellular automata}, Author = {Wolfram, S.}, Journal = {Commun. Math. Phys.}, Year = {1984}, Pages = {15--57}, Volume = {96}, DOI = {10.1007/BF01217347} } @Article{WolfSwift85, Title = {Determining {Lyapunov} exponents from a time series}, Author = {Wolf, A. and Swift, J. B. and Swinney, H. L. and Vastano, J. A.}, Journal = {Physica D}, Year = {1985}, Pages = {285--317}, Volume = {16}, DOI = {10.1016/0167-2789(85)90011-9} } @Article{WoSa07, Title = {An efficient method for recovering {Lyapunov} vectors from singular vectors}, Author = {Wolfe, C. L. and Samelson, R. M.}, Journal = {Tellus A}, Year = {2007}, Pages = {355--366}, Volume = {59}, DOI = {10.1111/j.1600-0870.2007.00234.x} } @Article{WRT92, Title = {The semiclassical helium atom}, Author = {Wintgen, D. and Richter, K. and Tanner, G.}, Journal = {Chaos}, Year = {1992}, Pages = {19--33}, Volume = {2}, DOI = {10.1063/1.165920} } @Article{Wu2010596, author = {Z.-D. Wu and T. Jiang and W.-J. Su}, title = {Efficient computation of shortest absent words in a genomic sequence}, journal = {Inform. Processing Lett.}, year = {2010}, volume = {110}, pages = {596--601}, doi = {10.1016/j.ipl.2010.05.008} } @Article{Wulff00, Title = {From relative equilibria to relative periodic orbits}, Author = {C. Wulff}, Journal = {Doc. Math.}, Year = {2000}, Pages = {227--274}, Volume = {5}, URL = {http://emis.ams.org/journals/DMJDMV/vol-05/09.pdf} } @Article{Wulff01, Title = {Bifurcation from relative periodic solutions}, Author = {Wulff, C. and Lamb, J. S. W. and Melbourne, I.}, Journal = {Ergod. Theor. Dynam. Syst.}, Year = {2001}, Pages = {605--635}, Volume = {21}, DOI = {10.1017/S0143385701001298} } @Article{Wulff03, author = {C. Wulff}, title = {Persistence of {Hamiltonian} relative periodic orbits}, journal = {J. Geometry and Physics}, year = {2003}, volume = {48}, pages = {309--338}, doi = {10.1016/S0393-0440(03)00046-9} } @Inproceedings{WW05, author = {F. Waleffe and J. Wang}, title = {Transition threshold and the {Self-Sustaining Process}}, booktitle = {{Non-uniqueness of Solutions to the {Navier-Stokes} Equations and their Connection with Laminar-Turbulent Transition}}, year = {2005}, editor = {T. Mullin and R. R. Kerswell}, pages = {85--106}, publisher = {Kluwer}, doi = {10.1007/1-4020-4049-0_5}, } @Article{WX94, author = {Y. Wang and H. Xie}, title = {Grammatical complexity of unimodal maps with eventually periodic kneading sequences}, journal = {Nonlinearity}, year = {1994}, volume = {7}, pages = {1419}, doi = {10.1088/0951-7715/7/5/009}, } @Article{Wylie07, author = {Cates Wylie, D.}, title = {Linked by loops: {Network} structure and switch integration in complex dynamical systems}, journal = {Physica A}, year = {2009}, volume = {388}, pages = {1946--1958}, doi = {10.1016/j.physa.2009.01.018} } @Article{XH94, author = {Xie, F.-G. and Hao, B. L.}, journal = {Physica A}, title = {Counting the number of periods in one-dimensional maps with multiple critical points}, year = {1994}, pages = {237--263}, volume = {202}, doi = {10.1016/0378-4371(94)90176-7}, } @Article{Xia92, Title = {Existence of invariant tori in volume-preserving diffeomorphisms}, Author = {Xia, Z.}, Journal = {Ergod. Theor. Dynam. Syst.}, Year = {1992}, Pages = {621--31}, Volume = {12}, DOI = {10.1017/S0143385700006969} } @Book{Yaglom88, title = {{Felix Klein and Sophus Lie: evolution of the idea of symmetry in the Nineteenth Century}}, publisher = {Birkh{\"a}user}, year = {1988}, author = {Yaglom, I. M. and Grant, H. and Shenitzer, A.}, isbn = {9783764333164}, doi = {10.2307/2686460}, } @Article{YaIsAk14, Title = {Stability analysis of large-scale dynamical systems by sub-{Gramian} approach}, Author = {Yadykin, I. B. and Iskakov, A. B. and Akhmetzyanov, A. V.}, Journal = {Int. J. Robust Nonlin. Control}, Year = {2014}, Pages = {1361--1379}, Volume = {24}, DOI = {10.1002/rnc.3116} } @Article{YaRa10, Title = {Comparison between covariant and orthogonal {Lyapunov} vectors}, Author = {Yang, H.-l. and Radons, G.}, Journal = {Phys. Rev. E}, Year = {2010}, Pages = {046204}, Volume = {82}, DOI = {10.1103/PhysRevE.82.046204} } @Article{YaTaGiChRa08, Title = {Hyperbolicity and the effective dimension of spatially-extended dissipative systems}, Author = {Yang, H.-l. and Takeuchi, K. A. and Ginelli, F. and Chat{\'e}, H. and Radons, G.}, Journal = {Phys. Rev. Lett.}, Year = {2009}, Pages = {074102}, Volume = {102}, DOI = {10.1103/PhysRevLett.102.074102} } @Book{Yode88, author = {J. G. Yoder}, publisher = {Cambridge Univ. Press}, title = {{Unrolling Time: {Christiaan Huygens} and the Mathematization of Nature}}, year = {1989}, address = {Cambridge UK}, doi = {10.1017/cbo9780511622441}, } @Article{YoNo93, Title = {Finite-time {Lyapunov} stability analysis and its application to atmospheric predictability}, Author = {Yoden, S. and Nomura, M.}, Journal = {J. Atmos. Sci.}, Year = {1993}, Pages = {1531--1543}, Volume = {50}, DOI = {10.1175/1520-0469(1993)050<1531:FTLSAA>2.0.CO;2} } @Article{Young1802, author = {T. Young}, title = {The {Bakerian Lecture}: {On} the theory of light and colours}, journal = {Phil. Trans. Roy. Soc.}, year = {1802}, volume = {92}, pages = {12--48}, doi = {10.1098/rstl.1802.0004}, } @Article{yu93bd, author = {S. V. Vladimirov and M. Y. Yu}, journal = {Phys. Fluids B}, title = {Boundary effects on the nonlinear interactions of surface waves}, year = {1993}, pages = {2888}, volume = {5}, doi = {10.1063/1.860676}, } @Article{yu94sur, author = {S. V. Vladimirov and M. Y. Yu}, title = {Nonlinear interaction of surface plasmons in electron slabs}, journal = {Phys. Lett. A}, year = {1994}, volume = {184}, pages = {459--463}, doi = {10.1016/0375-9601(94)90524-X}, } @Article{yuan00id, Title = {Testing whether two chaotic one dimensional processes are dynamically identical}, Author = {G.-C. Yuan and J. A. Yorke and T. L. Carroll and E. Ott and L. M. Pecora}, Journal = {Phys. Rev. Lett.}, Year = {2000}, Pages = {4265}, Volume = {85}, DOI = {10.1103/PhysRevLett.85.4265} } @Article{Za76, author = {P. E. Zadunaiski}, title = {On the estimation of errors propagated in the numerical integration of ordinary differential equations}, journal = {Numer. Math.}, year = {1976}, volume = {27}, pages = {21--39}, doi = {10.1007/bf01399082}, } @Article{Zagarola98, author = {M. V. Zagarola and A. J. Smits}, title = {Mean flow scaling of turbulent pipe flow}, journal = {J. Fluid Mech.}, year = {1998}, volume = {373}, pages = {33--79}, doi = {10.1017/s0022112098002419}, } @Article{Zang91, author = {T. A. Zang}, title = {On the rotation and skew-symmetric forms for incompressible flow simulations}, journal = {Appl. Numer. Math.}, year = {1991}, volume = {7}, pages = {27--40}, doi = {10.1016/0168-9274(91)90102-6}, } @Phdthesis{Zarrin06, Title = {{CUPOLETS}: {Chaotic} unstable periodic orbits theory and applications}, Author = {Zarringhalam, K.}, School = {Univ. New Hampshire}, Year = {2007} } @Article{ZarSho08, Title = {Generating an adaptive multiresolution image analysis with compact cupolets}, Author = {Zarringhalam, K. and Short, K. M.}, Journal = {Nonlin. Dyn.}, Year = {2008}, Pages = {51--70}, Volume = {52}, DOI = {10.1007/s11071-007-9257-7} } @Article{ZaZha70, Title = {Concentration wave propagation in 2-dimensional liquid-phase self-oscillating system}, Author = {Zaikin, A. N. and Zhabotinsky, A. M.}, Journal = {Nature}, Year = {1970}, Pages = {535--537}, Volume = {225}, DOI = {10.1038/225535b0} } @Article{Zeitak88, author = {I. Procaccia and R. Zeitak}, title = {Shape of fractal growth patterns: {Exactly} solvable models and stability considerations}, journal = {Phys. Rev. Lett.}, year = {1988}, volume = {60}, pages = {2511}, doi = {10.1103/PhysRevLett.60.2511} } @Article{ZeMa85, author = {Zeghlache, H. and Mandel, P.}, title = {Influence of detuning on the properties of laser equations}, journal = {J. Optical Soc. of America B}, year = {1985}, volume = {2}, pages = {18--22}, doi = {10.1364/josab.2.000018}, } @Article{ZG96, Title = {Spatially localized unstable periodic orbits of a high-dimensional chaotic system}, Author = {S. M. Zoldi and H. S. Greenside}, Journal = {Phys. Rev. E}, Year = {1998}, Pages = {R2511--R2514}, Volume = {57}, DOI = {10.1103/PhysRevE.57.R2511} } @Article{ZgRi01, author = {P. Zgliczynski and K. Mischaikow}, title = {Rigorous numerics for partial differential equations: {The Kuramoto-Sivashinsky} equation}, journal = {Found. Comp. Math.}, year = {2001}, volume = {1}, pages = {255--288}, doi = {10.1007/s002080010010}, } @Article{ZhaLan13, author = {Zhang, C. and Lan, Y.}, title = {Computation of growth rates of random sequences with multi-step memory}, journal = {J. Stat. Phys.}, year = {2013}, volume = {150}, pages = {722--743}, doi = {10.1007/s10955-013-0712-1}, } @Unpublished{ZhCvGo15, author = {Zhang, T. and Cvitanovi\'c, P. and Goldman, D. I.}, title = {Diffuse globally, compute locally: a cyclist tale}, note = {In preparation}, year = {2017}, } @Article{ZhLuRo01, author = {Z. Zheng and K. Lust and D. Roose}, title = {A numerical and analytical study of {F}loquet multipliers of periodic solutions near a homoclinic orbit}, journal = {Nonlinear Anal.}, year = {2001}, volume = {47}, pages = {3369--3378}, doi = {10.1016/s0362-546x(01)00452-7}, } @Article{Zhou92, author = {X. Zhou and L. Sirovich}, title = {Coherence and chaos in a model of turbulent boundary layer}, journal = {Phys. Fluids A}, year = {1992}, volume = {4}, pages = {2855--2874}, doi = {10.1063/1.858340}, } @Phdthesis{Zimmermann97, Title = {{Global Bifurcations and Chaotic Dynamics in Physical Applications}}, Author = {Zimmermann, M. G.}, School = {Uppsala Univ.}, Year = {1997}, ISBN = {9789155439729}, } @Book{Zinn-Justin89, title = {{Quantum Field Theory and Critical Phenomena}}, publisher = {Oxford Univ. Press}, year = {1989}, author = {J. Zinn-Justin}, address = {Oxford}, doi = {10.1093/acprof:oso/9780198509233.001.0001}, } @Article{ZumKla, author = {Zumofen, G. and Klafter, J.}, title = {Scale-invariant motion in intermittent chaotic systems}, journal = {Phys. Rev. A}, year = {1993}, volume = {47}, pages = {851}, doi = {10.1103/physreve.47.851}, } @Book{Zyg, author = {A. Zygmund}, publisher = {Cambridge Univ. Press}, title = {{Trigonometric Series}}, year = {1959}, address = {Cambridge UK}, doi = {10.1017/cbo9781316036587.002}, } @Article{LKKK16, author = {G. A. Leonov and N. V. Kuznetsov and N. A. Korzhemanova and D. V. Kusakin}, title = {Lyapunov dimension formula for the global attractor of the {Lorenz system}}, journal = {Commun. Nonlinear Sci. Numer. Simul.}, year = {2016}, volume = {41}, pages = {84--103}, doi = {10.1016/j.cnsns.2016.04.032}, } @Misc{wiki:Lorenz_system, author = {{Wikipedia contributors}}, title = {Lorenz system --- {Wikipedia, The Free Encyclopedia}}, year = {2020}, url = {https://en.wikipedia.org/wiki/Lorenz_system}, } @Article{McGuinness83, author = {M. J. McGuinness}, title = {The fractal dimension of the {Lorenz }attractor}, journal = {Phys. Lett. A}, year = {1983}, volume = {99}, pages = {5--9}, doi = {10.1016/0375-9601(83)90052-x}, } @Article{Doering_1995, author = {C. R. Doering and J. D. Gibbon}, title = {On the shape and dimension of the {Lorenz} attractor}, journal = {Dynamics and Stability of Systems}, year = {1995}, volume = {10}, pages = {255--268}, doi = {10.1080/02681119508806207}, } @Article{LeoBoi92, author = {G. A. Leonov and V. A. Boichenko}, title = {Lyapunov's direct method in the estimation of the {Hausdorff} dimension of attractors}, journal = {Acta Appl Math}, year = {1992}, volume = {26}, pages = {1--60}, doi = {10.1007/bf00046607}, } @Article{LePoSt11, author = {G.A. Leonov and A.Yu. Pogromsky and K.E. Starkov}, title = {The dimension formula for the {Lorenz} attractor}, journal = {Phys. Lett. A}, year = {2011}, volume = {375}, pages = {1179--1182}, doi = {10.1016/j.physleta.2011.01.034}, } @InCollection{Ghys13, author = {Ghys, {\'{E}}.}, booktitle = {{Chaos}}, publisher = {Springer}, title = {The {Lorenz} attractor, a paradigm for chaos}, year = {2013}, address = {New York}, editor = {Duplantier, B. and Nonnenmacher, S. and Rivasseau, V.}, pages = {1--54}, doi = {10.1007/978-3-0348-0697-8_1}, } @Article{GraElg04, author = {S. Gratrix and J. N. Elgin}, title = {Pointwise dimensions of the {Lorenz} attractor}, journal = {Phys. Rev. Lett.}, year = {2004}, volume = {92}, pages = {014101}, doi = {10.1103/physrevlett.92.014101}, } @Article{WikElg96, author = {K. O. Wiklund and J. N. Elgin}, title = {Multifractality of the {Lorenz} system}, journal = {Phys. Rev. E}, year = {1996}, volume = {54}, pages = {1111--1119}, doi = {10.1103/physreve.54.1111}, } @Article{OtSaYo89, author = {E. Ott and T. Sauer and J. A. Yorke}, title = {Lyapunov partition functions for the dimensions of chaotic sets}, journal = {Phys. Rev. A}, year = {1989}, volume = {39}, pages = {4212--4222}, doi = {10.1103/physreva.39.4212}, } @Book{PMM1824, title = {{En Dansk Students Eventyr [The Adventures of a Danish Student]}}, publisher = {Schubotheske Forlag}, year = {1824}, author = {M{\o}ller, P. M.}, isbn = {9788740431803}, series = {Schubotheske miniatur-bibliotek}, url = {https://play.google.com/store/books/details?id=aNVJAQAAMAAJ}, } @Book{Adams79, title = {{The Ultimate Hitchhiker's Guide to the Galaxy}}, publisher = {Random House}, year = {1979}, author = {Adams, D.}, isbn = {9780307498465}, address = {New York}, } @Article{Kadanoff86, author = {L. P. Kadanoff}, title = {Fractals: where's the physics?}, journal = {Phys. Today}, year = {1986}, volume = {39}, pages = {6}, doi = {10.1063/1.2814878}, } @Article{Venegeroles08, author = {R. Venegeroles}, title = {Calculation of superdiffusion for the {Chirikov-Taylor} model}, journal = {Phys. Rev. Lett.}, year = {2008}, volume = {101}, pages = {054102}, doi = {10.1103/physrevlett.101.054102}, } @PhdThesis{SandersPhD05, author = {D. P. Sanders}, title = {{Deterministic Diffusion in Periodic Billiard Models}}, school = {Mathematics, Univ. of Warwick}, year = {2005}, url = {https://arXiv.org/abs/0808.2252}, } @Article{IooMon95, author = {J. Montaldi}, title = {Persistence of relative periodic orbits in symmetric {Hamiltonian} systems}, journal = {Compt. Rend. Acad. Sci., Math. (Paris)}, year = {1997}, volume = {324}, pages = {553--558}, doi = {10.1016/s0764-4442(99)80389-9}, } @Article{GuiUri89, author = {V. Guillemin and A. Uribe}, title = {Circular symmetry and the trace formula}, journal = {Inv. Math.}, year = {1989}, volume = {96}, pages = {385--423}, doi = {10.1007/bf01393968}, } @Article{BPPV, author = {R. Benzi and G. Paladin and G. Parisi and A. Vulpiani}, title = {Characterisation of intermittency in chaotic systems}, journal = {J. Phys. A}, year = {1985}, volume = {18}, pages = {2157--2165}, doi = {10.1088/0305-4470/18/12/013}, } @Article{Dirac33, author = {P. A. M. Dirac}, title = {The {Lagrangian} in quantum mechanics}, journal = {Phys. Z. SowjUn.}, year = {1933}, volume = {3}, pages = {64--72}, doi = {10.1142/9789812567635_0003}, } @Article{Fox78, author = {Fox, R. F.}, title = {{Gaussian} stochastic processes in physics}, journal = {Phys. Rep.}, year = {1978}, volume = {48}, pages = {179--283}, doi = {10.1016/0370-1573(78)90145-X}, } @Article{HakenM-K81, author = {H. Haken and G. Mayer-Kress}, title = {{Chapman-Kolmogorov} equation and path integrals for discrete chaos in presence of noise}, journal = {Z. f. Physik B}, year = {1981}, volume = {43}, pages = {185--187}, doi = {10.1007/bf01293609}, } @Book{Kac59, title = {{Probability and Related Topics in Physical Sciences}}, publisher = {Amer. Math. Soc.}, year = {1959}, author = {Kac, M.}, isbn = {9780821800478}, } @Article{Kif74, author = {Yu. I. Kifer}, title = {On small random perturbations of some smooth dynamical systems}, journal = {Math. USSR-Izv.}, year = {1974}, volume = {8}, pages = {1083--1107}, doi = {10.1070/im1974v008n05abeh002139}, } @Book{Pontr62, author = {Pontrjagin, L. S. and Boltyanskii, V. and Gamkrelidge, R. and Mishenko, E.}, publisher = {Interscience Publishers}, title = {{The Mathematical Theory of Optimal Processes}}, year = {1964}, address = {New York}, isbn = {9782881240775}, } @Book{LRT13, title = {{Functional Integration and Semiclassical Expansions}}, publisher = {Springer}, year = {1982}, author = {Langouche, F. and Roekaerts, D. and Tirapegui, E.}, isbn = {9789401716345}, address = {New York}, doi = {10.1007/978-94-017-1634-5}, } @Article{Jakobson81, author = {M. V. Jakobson}, title = {Absolutely continuous invariant measures for one-parameter families of one-dimensional maps}, journal = {Commun. Math. Phys.}, year = {1981}, volume = {81}, pages = {39--88}, doi = {10.1007/BF01941800}, } @Article{moser96, author = {J. Moser}, title = {A rapidly converging iteration method and nonlinear partial differential equations {I.}}, journal = {Ann. Scuola Norm. Super. Pisa}, year = {1966}, volume = {20}, pages = {265--315}, url = {http://www.numdam.org/item?id=ASNSP_1966_3_20_2_265_0}, } @Article{moser96a, author = {J. Moser}, title = {A rapidly converging iteration method and nonlinear partial differential equations {II.}}, journal = {Ann. Scuola Norm. Super. Pisa}, year = {1966}, volume = {20}, pages = {499--535}, url = {http://www.numdam.org/numdam-bin/item?id=ASNSP_1966_3_20_3_499_0}, } @Article{Mo86b, author = {Moser, J.}, title = {Recent developments in the theory of {Hamiltonian} systems}, journal = {SIAM Rev.}, year = {1986}, volume = {28}, pages = {459--485}, doi = {10.1137/1028153}, } @Article{moser86, author = {J. Moser}, title = {Minimal solutions of variational problems on a torus}, journal = {Ann. Inst. H. Poincar{\'e} Anal. Non Lin{\'e}aire}, year = {1986}, volume = {3}, pages = {229--272}, url = {http://www.numdam.org/numdam-bin/item?id=AIHPC_1986__3_3_229_0}, } @Article{HMWRW88, author = {A. Holle and J. Main and G. Wiebusch and H. Rottke and K. H. Welge}, title = {Quasi-{Landau} spectrum of the chaotic diamagnetic hydrogen atom}, journal = {Phys. Rev. Lett.}, year = {1988}, volume = {61}, pages = {161--164}, doi = {10.1103/physrevlett.61.161}, } @Article{PolVyt16, author = {M. Pollicott and P. Vytnova}, title = {Linear response and periodic points}, journal = {Nonlinearity}, year = {2016}, volume = {29}, pages = {3047--3066}, doi = {10.1088/0951-7715/29/10/3047}, } @Misc{CviSon98, author = {P. Cvitanovi{\'c}}, title = {Periodic orbit formulation of linear response (working notes for {N. S{\o}ndergaard})}, year = {1998}, url = {http://ChaosBook.org/~predrag/papers/unfinished.html}, } @Article{BedSmi16, author = {E. Bedford and J. Smillie}, journal = {Ergod. Theor. Dynam. Syst.}, title = {A symbolic characterization of the horseshoe locus in the {H{\'{e}}non} family}, year = {2016}, pages = {1--24}, doi = {10.1017/etds.2015.113}, } @Article{LiXie16, author = {D. Li and J. Xie}, title = {Symbolic dynamics of {Belykh}-type maps}, journal = {Appl. Math. Mech.}, year = {2016}, volume = {37}, pages = {671--682}, doi = {10.1007/s10483-016-2080-9}, } @Article{CaGrRo09, author = {A. Caneco and C. Gr{\'{a}}cio and J. L. Rocha}, title = {Kneading theory analysis of the {Duffing} equation}, journal = {Chaos Solit. Fract.}, year = {2009}, volume = {42}, pages = {1529--1538}, doi = {10.1016/j.chaos.2009.03.040}, } @Article{JaeKan97, author = {L. Jaeger and H. Kantz}, title = {Structure of generating partitions for two-dimensional maps}, journal = {J. Phys. A}, year = {1997}, volume = {30}, pages = {L567--L576}, doi = {10.1088/0305-4470/30/16/003}, } @Article{Tel83, author = {T. T{\'{e}}l}, title = {Fractal dimension of the strange attractor in a piecewise linear two-dimensional map}, journal = {Phys. Lett. A}, year = {1983}, volume = {97}, pages = {219--223}, doi = {10.1016/0375-9601(83)90751-x}, } @Article{GlaLib88, author = {J.A. Glazier and A. Libchaber}, title = {Quasi-periodicity and dynamical systems: {An} experimentalist's view}, journal = {{IEEE} Trans. Circuits and Systems}, year = {1988}, volume = {35}, pages = {790--809}, doi = {10.1109/31.1826}, } @Article{Knauf93, author = {Knauf, A.}, title = {On a ferromagnetic spin chain}, journal = {Commun. Math. Phys.}, year = {1993}, volume = {153}, pages = {77--115}, doi = {10.1007/bf02099041}, } @Article{FeKaSh82, author = {M. J. Feigenbaum and L. P. Kadanoff and S. J. Shenker}, title = {Quasiperiodicity in dissipative systems: {A} renormalization group analysis}, journal = {Physica D}, year = {1982}, volume = {5}, pages = {370--386}, doi = {10.1016/0167-2789(82)90030-6}, } @Article{Feigenbaum_1982, author = {M. J. Feigenbaum and L. P. Kadanoff and S. J. Shenker}, title = {Quasiperiodicity in dissipative systems: {A} renormalization group analysis}, journal = {Physica D}, year = {1982}, volume = {5}, pages = {370--386}, doi = {10.1016/0167-2789(82)90030-6}, } @Article{RaOsSeSi82, author = {D. Rand and S. Ostlund and J. Sethna and E. D. Siggia}, title = {Universal transition from quasiperiodicity to chaos in dissipative systems}, journal = {Phys. Rev. Lett.}, year = {1982}, volume = {49}, pages = {132--135}, doi = {10.1103/physrevlett.49.132}, } @Article{SeOsRaSi83, author = {S. Ostlund and D. Rand and J. Sethna and E. Siggia}, title = {Universal properties of the transition from quasi-periodicity to chaos in dissipative systems}, journal = {Physica D}, year = {1983}, volume = {8}, pages = {303--342}, doi = {10.1016/0167-2789(83)90229-4}, } @Article{CSS85, author = {P. Cvitanovi{\'c} and B. Shraiman and B. S\"oderberg}, title = {Scaling laws for mode lockings in circle maps}, journal = {Phys. Scr.}, year = {1985}, volume = {32}, pages = {263--270}, doi = {10.1088/0031-8949/32/4/003}, } @Misc{moron, author = {Bensimon, D. and Halsey, T. C. and Jensen, M. H. and Kadanoff, L. P. and Libchaber, A. and Procaccia, I. and Shraiman, B. I. and Stavans, J.}, note = {Rejected from all proceedings it was submitted to}, title = {More on microcanonical paradigm}, year = {1986}, address = {G{\"o}teborg}, url = {http://ChaosBook.org/~predrag/papers/preprints.html#moron}, } @Article{Swiatek88, author = {G. {\'{S}}wi{\k{a}}tek}, title = {Rational rotation numbers for maps of the circle}, journal = {Commun. Math. Phys.}, year = {1988}, volume = {119}, pages = {109--128}, doi = {10.1007/bf01218263}, } @Article{ACK89, author = {Artuso, R. and Cvitanovi{\'c}, P. and Kenny, B. G.}, title = {Phase transitions on strange irrational sets}, journal = {Phys. Rev. A}, year = {1989}, volume = {39}, pages = {268--281}, doi = {10.1103/PhysRevA.39.268}, } @Article{StHeLi85, author = {J. Stavans and F. Heslot and A. Libchaber}, title = {Fixed winding number and the quasiperiodic route to chaos in a convective fluid}, journal = {Phys. Rev. Lett.}, year = {1985}, volume = {55}, pages = {596--599}, doi = {10.1103/physrevlett.55.596}, } @Article{GwiWes87, author = {E. G. Gwinn and R. M. Westervelt}, title = {Scaling structure of attractors at the transition from quasiperiodicity to chaos in electronic transport in {Ge}}, journal = {Phys. Rev. Lett.}, year = {1987}, volume = {59}, pages = {157--160}, doi = {10.1103/physrevlett.59.157}, } @Article{KimOst89, author = {S. Kim and S. Ostlund}, title = {Universal scaling in circle maps}, journal = {Physica D}, year = {1989}, volume = {39}, pages = {365--392}, doi = {10.1016/0167-2789(89)90017-1}, } @Article{Kaneko83, author = {Kaneko, K.}, title = {Transition from torus to chaos accompanied by frequency lockings with symmetry breaking: {In} connection with the coupled-logistic map}, journal = {Progr. Theor. Phys.}, year = {1983}, volume = {69}, pages = {1427--1442}, doi = {10.1143/PTP.69.1427}, } @Article{Kaneko84, author = {Kaneko, K.}, title = {Period-doubling of kink-antikink patterns, quasiperiodicity in antiferro-like structures and spatial intermittency in coupled logistic lattice: {Towards} a prelude of a ``field theory of chaos''}, journal = {Progr. Theor. Phys.}, year = {1984}, volume = {72}, pages = {480--486}, doi = {10.1143/PTP.72.480}, } @Article{Kaneko83a, author = {K. Kaneko}, title = {Similarity structure and scaling property of the period-adding phenomena}, journal = {Progr. Theor. Phys.}, year = {1983}, volume = {69}, pages = {403--414}, doi = {10.1143/ptp.69.403}, } @Article{Kaneko82, author = {K. Kaneko}, title = {On the period-adding phenomena at the frequency locking in a one-dimensional mapping}, journal = {Progr. Theor. Phys.}, year = {1982}, volume = {68}, pages = {669--672}, doi = {10.1143/ptp.68.669}, } @Book{LifPit, author = {Pitaevskii, L. P. and Lifshitz, E. M.}, publisher = {Elsevier}, title = {{Physical Kinetics}}, year = {1981}, isbn = {9780750626354}, } @Article{Jac96, author = {M. Jacobsen}, title = {Laplace and the origin of the {Ornstein-Uhlenbeck} process}, journal = {Bernoulli}, year = {1996}, volume = {2}, pages = {271}, doi = {10.2307/3318524}, } @Article{Ito, author = {K. It\^{o}}, title = {Stochastic integral}, journal = {Proc. Imp. Acad. Tokyo}, year = {1944}, volume = {20}, pages = {519--524}, doi = {10.3792/pia/1195572786}, } @Article{BuMoMe12, author = {Budi{\v s}i{\'c}, M. and Mohr, R. M. and Mezi{\'c}, I.}, title = {{Applied Koopmanism}}, journal = {Chaos}, year = {2012}, volume = {22}, pages = {047510}, doi = {10.1063/1.4772195}, } @Article{BudMez12, author = {M. Budi\v{s}i\'c and I. Mezi\'c}, title = {Geometry of the ergodic quotient reveals coherent structures in flows}, journal = {Physica D}, year = {2012}, volume = {241}, pages = {1255--1269}, doi = {10.1016/j.physd.2012.04.006}, } @Article{RoMeBaSchHe09, author = {Rowley, C. W. and Mezi\'c, I. and Bagheri, S. and Schlatter, P. and Henningson, D. S.}, title = {Spectral analysis of nonlinear flows}, journal = {J. Fluid Mech.}, year = {2009}, volume = {641}, pages = {115}, doi = {10.1017/s0022112009992059}, } @Article{LevnMezi08, author = {Levnaji{\'c}, Z. and Mezi{\'c}, I.}, title = {Ergodic theory and visualization. {I. Mesochronic} plots for visualization of ergodic partition and invariant sets}, journal = {Chaos}, year = {2010}, volume = {20}, pages = {033114}, doi = {10.1063/1.3458896}, } @Book{Mezic17, title = {{Spectral Koopman Operator Methods in Dynamical Systems}}, publisher = {Springer}, year = {2017}, author = {Mezi\'c, I.}, address = {New York}, note = {In preparation}, } @Article{LevnMezi15, author = {Levnaji\'c, Z. and Mezi\'c, I.}, title = {Ergodic theory and visualization. {II}. {Fourier }mesochronic plots visualize (quasi)periodic sets}, journal = {Chaos}, year = {2015}, volume = {25}, pages = {053105}, doi = {10.1063/1.4919767}, } @Misc{BuDiCv15, author = {Budanur, N. B. and Ding, D. and Cvitanovi\'c, P.}, title = {Turbulent {Kuramoto-Sivashinsky} system recycled}, year = {2015}, note = {In preparation}, } @Article{vN32, author = {J. von Neumann}, title = {{Zur Operatorenmethode In Der Klassischen Mechanik}}, journal = {Ann. Math.}, year = {1932}, volume = {33}, pages = {587--642}, note = {See additions \cite{vonNeum32}. Reprinted in \cite{Taub61}.}, doi = {10.2307/1968537}, } @Book{Taub61, title = {{{John von Neumann}: Collected Works. {Volume II}: {Operators}, Ergodic Theory and Almost Periodic Functions in a Group}}, publisher = {Pergamon Press}, year = {1961}, editor = {A. H. Taub}, address = {New York}, } @Article{Sylvester1852, author = {Sylvester, J. J.}, journal = {Philos. Mag.}, pages = {138--142}, title = {{XIX}. {A} demonstration of the theorem that every homogeneous quadratic polynomial is reducible by real orthogonal substitutions to the form of a sum of positive and negative squares}, volume = {4}, year = {1852}, doi = {10.1080/14786445208647087}, } @Article{Voros92, author = {Voros, A.}, title = {Spectral zeta functions}, journal = {Adv. Stud. Pure Math}, year = {1992}, volume = {21}, pages = {327--358}, } @Article{Hurt93a, author = {Hurt, N. E.}, title = {Three topics on periodic orbit theory: {A} review}, journal = {Rev. Math. Phys.}, year = {1993}, volume = {5}, pages = {713--733}, doi = {10.1142/s0129055x9300022x}, } @InProceedings{Fried87, author = {Fried, D.}, title = {Lefschetz formulas for flows}, booktitle = {{The Lefschetz Centennial Conference}}, year = {1987}, editor = {D. Sundararaman and A. Verjovsky and S. Gitler}, volume = {58}, pages = {41--43}, address = {Providence, RI}, publisher = {AMS}, doi = {10.1090/conm/058.3}, } @Article{CE91, author = {Cvitanovi{\'c}, P. and Eckhardt, B.}, journal = {J. Phys. A}, title = {Periodic orbit expansions for classical smooth flows}, year = {1991}, pages = {L237--L241}, volume = {24}, doi = {10.1088/0305-4470/24/5/005}, } @Misc{LiHuCa10, author = {Libert, A.-S. and Hubaux, C. and Carletti, T.}, title = {Symplectic integration of deviation vectors and chaos determination. Application to the {H{\'e}non-Heiles} model and to the restricted three-body problem}, year = {2010}, eprint = {1005.5611}, eprinttype = {arxiv}, } @Article{Wimmer73, author = {H. K. Wimmer}, title = {{On the Ostrowski-Schneider Inertia Theorem}}, journal = {J. Math. Anal. Appl.}, year = {1973}, volume = {41}, pages = {164--169}, doi = {10.1016/0022-247x(73)90190-x}, } @Article{CarlSchn62, author = {D. Carlson and H. Schneider}, title = {Inertia theorems for matrices: the semi-definite case}, journal = {Bull. Amer. Math. Soc.}, year = {1962}, volume = {68}, pages = {479--484}, doi = {10.1090/s0002-9904-1962-10784-8}, publisher = {American Mathematical Society ({AMS})}, } @Article{OsSchn62, author = {A. Ostrowski and H. Schneider}, title = {Some theorems on the inertia of general matrices}, journal = {J. Math. Anal. Appl.}, year = {1962}, volume = {4}, pages = {72--84}, doi = {10.1007/978-3-0348-9355-8_37}, } @Article{AnSo01, author = {Antoulas, A. C. and Sorensen, D. C.}, journal = {Linear Algebra Appl.}, title = {{Lyapunov}, {Lanczos}, and inertia}, year = {2001}, pages = {137--150}, volume = {326}, doi = {10.1016/s0024-3795(00)00288-3}, } @Article{Ort00, author = {J.-P. Ortega and T. S. Ratiu}, title = {A {Dirichlet} criterion for the stability of periodic and relative periodic orbits in {Hamiltonian} systems}, journal = {J. Geometry and Physics}, year = {1999}, volume = {32}, pages = {131--159}, doi = {10.1016/s0393-0440(99)00025-x}, } @Article{Lanford85, author = {O. E. Lanford}, title = {A numerical study of the likelihood of phase locking}, journal = {Physica D}, year = {1985}, volume = {14}, pages = {403--408}, doi = {10.1016/0167-2789(85)90099-5}, } @PhdThesis{mest, author = {B. D. Mestel}, title = {Computer assisted proof of universality of cubic critical maps of the circle with golden mean rotation number}, school = {University of Warwick}, year = {1985}, } @Article{Kim_1989, author = {S. Kim and S. Ostlund}, title = {Universal scaling in circle maps}, journal = {Physica D}, year = {1989}, volume = {39}, pages = {365--392}, doi = {10.1016/0167-2789(89)90017-1}, } @Article{Tsygvintsev_2002, author = {A. V. Tsygvintsev and B. D. Mestel and A. H. Osbaldestin}, title = {Continued fractions and solutions of the {Feigenbaum-Cvitanovi{\'{c}}} equation}, journal = {Compt. Rend. Acad. Sci., Math. (Paris)}, year = {2002}, volume = {334}, pages = {683--688}, doi = {10.1016/s1631-073x(02)02330-0}, } @Misc{IsaKuz05b, author = {O. B. Isaeva and S. P. Kuznetsov}, title = {Period tripling accumulation point for complexified {H{\'e}non} map}, year = {2005}, url = {https://arXiv.org/abs/nlin.CD/0509012}, } @Misc{IsaKuz05a, author = {Isaeva, O. B. and Kuznetsov, S. P.}, title = {On possibility of realization of the {Mandelbrot} set in coupled continuous systems}, year = {2005}, url = {https://arXiv.org/abs/nlin/0509013}, } @Misc{BBMandelb, author = {P. Cvitanovi{\'c}}, title = {Reflections on {Benoit B. Mandelbrot}}, year = {2017}, url = {http://ChaosBook.org/~predrag/friends/Mandelbrot}, } @Article{Peckham_2000, author = {B. B. Peckham and J. Montaldi}, title = {Real continutation from the complex quadratic family: fixed point bifurcation sets}, journal = {Int. J. Bifur. Chaos}, year = {2000}, volume = {10}, pages = {391--414}, doi = {10.1142/s0218127400000256}, } @Book{edwa, title = {{Riemann's Zeta Function}}, publisher = {Dover}, year = {2003}, author = {H. M. Edwards}, address = {New York}, isbn = {9780486417400}, } @Book{Titchmarsh1986, title = {{The Theory of the Riemann Zeta-function}}, publisher = {Clarendon Press}, year = {1986}, author = {E. C. Titchmarsh and D. R. Heath-Brown}, isbn = {9780198533696}, address = {Oxford UK}, } @Article{Williams_1947, author = {G. T. Williams and D. H. Browne}, title = {A family of integers and a theorem on circles}, journal = {Amer. Math. Monthly}, year = {1947}, volume = {54}, pages = {534}, doi = {10.2307/2304669}, } @Article{DaHaNeI74, author = {Dashen, R. F. and Hasslacher, B. and Neveu, A.}, title = {Nonperturbative methods and extended-hadron models in field theory. {I}. {Semiclassical} functional methods}, journal = {Phys. Rev. D}, year = {1974}, volume = {10}, pages = {4114--4129}, doi = {10.1103/PhysRevD.10.4114}, } @Article{ConKna97, author = {P. Contucci and A. Knauf}, title = {The phase transition of the number-theoretical spin chain}, journal = {Forum Mathematicum}, year = {1997}, volume = {9}, pages = {547--568}, doi = {10.1515/form.1997.9.547}, } @Article{Csord_s_1989, author = {A. Csord{\'{a}}s and P. Sz{\'{e}}pfalusy}, title = {Dynamical multifractal properties of a map related to a chaotic cosmological model}, journal = {Phys. Rev. A}, year = {1989}, volume = {40}, pages = {2221--2224}, doi = {10.1103/physreva.40.2221}, } @Article{Levin72, author = {D. Levin}, title = {Development of non-linear transformations for improving convergence of sequences}, journal = {Int. J. Comput. Math.}, year = {1972}, volume = {3}, pages = {371--388}, doi = {10.1080/00207167308803075}, } @Article{Osada90, author = {N. Osada}, title = {A convergence acceleration method for some logarithmically convergent sequences}, journal = {{SIAM} J. Numer. Anal.}, year = {1990}, volume = {27}, pages = {178--189}, doi = {10.1137/0727012}, } @Article{Veerman_1986, author = {P. Veerman}, title = {Symbolic dynamics and rotation numbers}, journal = {Physica A}, year = {1986}, volume = {134}, pages = {543--576}, doi = {10.1016/0378-4371(86)90015-4}, } @Article{Veerman91, author = {J. J. P. Veerman and F. M. Tangerman}, title = {Intersection properties of invariant manifolds in certain twist maps}, journal = {Commun. Math. Phys.}, year = {1991}, volume = {139}, pages = {245--265}, doi = {10.1007/bf02352495}, } @Article{Zheng91, author = {W.-M. Zheng}, title = {Symbolic dynamics for the circle map}, journal = {Int. J. Mod. Phys. B}, year = {1991}, volume = {5}, pages = {481--495}, doi = {10.1142/s0217979291000298}, } @Article{Meiss_1986, author = {J. D. Meiss}, title = {Class renormalization: {Islands} around islands}, journal = {Phys. Rev. A}, year = {1986}, volume = {34}, pages = {2375--2383}, doi = {10.1103/physreva.34.2375}, } @Article{Afraimovich_2000, author = {V. Afraimovich and A. Maass and J. Ur{\'i}as}, title = {Symbolic dynamics for sticky sets in {Hamiltonian} systems}, journal = {Nonlinearity}, year = {2000}, volume = {13}, pages = {617--637}, doi = {10.1088/0951-7715/13/3/306}, } @Article{Meiss86b, author = {J. D. Meiss and E. Ott}, title = {Markov tree model of transport in area-preserving maps}, journal = {Physica D}, year = {1986}, volume = {20}, pages = {387--402}, doi = {10.1016/0167-2789(86)90041-2}, } @Article{Yampolsky_2003, author = {M. Yampolsky}, title = {On the eigenvalues of a renormalization operator}, journal = {Nonlinearity}, year = {2003}, volume = {16}, pages = {1565--1571}, doi = {10.1088/0951-7715/16/5/301}, } @Article{PerViv87b, author = {I. Percival and F. Vivaldi}, title = {Arithmetical properties of strongly chaotic motions}, journal = {Physica D}, year = {1987}, volume = {25}, pages = {105--130}, doi = {10.1016/0167-2789(87)90096-0}, } @Article{DV00, author = {Viswanath, D.}, journal = {Math. Comp.}, title = {Random {Fibonacci} sequences and the number 1.13198824...}, year = {2000}, pages = {1131--1155}, volume = {69}, doi = {10.1090/S0025-5718-99-01145-X}, } @InCollection{Visw07a, author = {D. Viswanath}, title = {The dynamics of transition to turbulence in plane {Couette} flow}, booktitle = {{Mathematics and Computation, a Contemporary View}}, publisher = {Springer}, year = {2008}, pages = {109--127}, address = {New York}, doi = {10.1007/978-3-540-68850-1_6}, } @Article{RanGla87, author = {Rand, D. A. and Glass, L.}, journal = {Proc. R. Soc. Lond. A}, title = {Fractal bifurcation sets, renormalization strange sets and their universal invariants}, year = {1987}, pages = {45--61}, volume = {413}, doi = {10.1098/rspa.1987.0099}, } @Article{Rand88, author = {D A Rand}, title = {Global phase space universality, smooth conjugacies and renormalisation. {I. The $C^{1+\alpha}$} case}, journal = {Nonlinearity}, year = {1988}, volume = {1}, pages = {181--202}, doi = {10.1088/0951-7715/1/1/007}, } @Article{Manneville80, author = {P. Manneville}, title = {Intermittency, self-similarity and 1/f spectrum in dissipative dynamical systems}, journal = {J. Phys. (Paris)}, year = {1980}, volume = {41}, pages = {1235--1243}, doi = {10.1051/jphys:0198000410110123500} } @Article{FeigenbaumMashed, author = {M. J. Feigenbaum and M. H. Jensen and I. Procaccia}, title = {Time ordering and the thermodynamics of strange sets: {Theory} and experimental tests}, journal = {Nucl. Phys. B Proc. Suppl.}, year = {1987}, volume = {2}, pages = {497--500}, doi = {10.1016/0920-5632(87)90035-1}, } @Article{WintgenHatom, author = {D. Wintgen}, title = {Connection between long-range correlations in quantum spectra and classical periodic orbits}, journal = {Phys. Rev. Lett.}, year = {1987}, volume = {58}, pages = {1589--1592}, doi = {10.1103/physrevlett.58.1589}, } @Article{BakerLongRange, author = {G. A. Baker}, title = {One-dimensional order-disorder model which approaches a second order phase transition}, journal = {Phys. Rev.}, year = {1961}, volume = {122}, pages = {1477--1484}, doi = {10.1103/physrev.122.1477}, } @Book{PikPol16, author = {Pikovsky, A. and Politi, A.}, publisher = {Cambridge Univ. Press}, title = {{Lyapunov Exponents: A Tool to Explore Complex Dynamics}}, year = {2016}, address = {Cambridge UK}, isbn = {9781316467701}, doi = {10.1017/cbo9781139343473}, } @Article{deva78, author = {R. L Devaney}, title = {Nonregularizability of the anisotropic {Kepler} problem}, journal = {J. Diff. Eqn.}, year = {1978}, volume = {29}, pages = {253--268}, doi = {10.1016/0022-0396(78)90124-9}, } @Article{Devaney1978, author = {R. L. Devaney}, journal = {Inv. Math.}, title = {Collision orbits in the anisotropic {Kepler} problem}, year = {1978}, pages = {221--251}, volume = {45}, doi = {10.1007/bf01403170}, } @Book{nonlin, title = {{Nonlinear Evolution and Chaotic Phenomena}}, publisher = {Springer}, year = {1988}, author = {G. Gallavotti and P. F. Zweifel}, address = {New York}, doi = {10.1007/978-1-4613-1017-4}, } @Article{Rechester1981, author = {A. B. Rechester and M. N. Rosenbluth and R. B. White}, title = {Fourier-space paths applied to the calculation of diffusion for the {Chirikov-Taylor} model}, journal = {Phys. Rev. A}, year = {1981}, volume = {23}, pages = {2664--2672}, doi = {10.1103/physreva.23.2664}, } @Article{Chen1989, author = {Q. Chen and J. D. Meiss}, title = {Flux, resonances and the devil's staircase for the sawtooth map}, journal = {Nonlinearity}, year = {1989}, volume = {2}, pages = {347--356}, doi = {10.1088/0951-7715/2/2/009}, } @InCollection{cvitanovic1988phase, author = {Cvitanovi{\'c}, P.}, title = {Phase transitions on strange sets}, booktitle = {{Nonlinear Evolution and Chaotic Phenomena}}, publisher = {Springer}, year = {1988}, editor = {Gallavotti, G. and Zweifel, P. F.}, volume = {176}, pages = {37--54}, address = {New York}, doi = {10.1007/978-1-4613-1017-4_4}, isbn = {978-1-4612-8294-5}, } @Article{Atmanspacher16, author = {H. Atmanspacher}, title = {On macrostates in complex multi-scale systems}, journal = {Entropy}, year = {2016}, volume = {18}, pages = {426}, doi = {10.3390/e18120426}, } @Article{BHJ12, author = {R. Band and J. M. Harrison and C. H. Joyner}, title = {Finite pseudo orbit expansions for spectral quantities of quantum graphs}, journal = {J. Phys. A}, year = {2012}, volume = {45}, pages = {325204}, doi = {10.1088/1751-8113/45/32/325204}, } @Article{WGTR13, author = {D. Waltner and S. Gnutzmann and G. Tanner and K. Richter}, title = {Subdeterminant approach for pseudo-orbit expansions of spectral determinants in quantum maps and quantum graphs}, journal = {Phys. Rev. E}, year = {2013}, volume = {87}, pages = {052919}, doi = {10.1103/physreve.87.052919}, } @Article{Boyd07, author = {Boyd, J. P.}, title = {Why {Newton}'s method is hard for travelling waves: small denominators, {KAM} theory, {Arnold}'s linear {Fourier} problem, non-uniqueness, constraints and erratic failure}, journal = {Math. Comput. Simulation}, year = {2007}, volume = {74}, pages = {72--81}, doi = {10.1016/j.matcom.2006.10.001}, } @Article{ByMaGr14, author = {Byrne, G. and Marcotte, C. D. and Grigoriev, R. O.}, title = {Exact coherent structures and chaotic dynamics in a model of cardiac tissue}, journal = {Chaos}, year = {2015}, volume = {25}, pages = {033108}, doi = {10.1063/1.4915143}, } @Incollection{KapYor79a, author = {Kaplan, J. L. and Yorke, J. A.}, title = {Chaotic behavior of multidimensional difference equations}, booktitle = {{Functional Differential Equations and Approximation of Fixed Points}}, publisher = {Springer}, year = {1979}, editor = {Peitgen, H.-O. and Walther, H.-O.}, volume = {730}, series = {Lect. Notes Math.}, pages = {204--227}, address = {Berlin}, doi = {10.1007/BFb0064320}, } @InCollection{Sandstede02, author = {Sandstede, B.}, title = {Stability of travelling waves}, booktitle = {{Handbook of Dynamical Systems, Vol. 2}}, publisher = {Elsevier}, year = {2002}, editor = {B. Fiedler}, pages = {983--1055}, address = {Amsterdam}, doi = {10.1016/S1874-575X(02)80039-X}, url = {http://www.dam.brown.edu/people/sandsted/publications/survey-stability-of-waves.pdf}, } @Article{TSYTES15, author = {Totz, J. F. and Snari, R. and Yengi, D. and Tinsley, M. R. and Engel, H. and Showalter, K.}, title = {Phase-lag synchronization in networks of coupled chemical oscillators}, journal = {Phys. Rev. E}, year = {2015}, volume = {92}, pages = {022819}, doi = {10.1103/PhysRevE.92.022819}, } @Article{GaRuBa10, author = {Garlaschelli, D. and Ruzzenenti, F. and Basosi, R.}, title = {Complex networks and symmetry: {A} review}, journal = {Symmetry}, year = {2010}, volume = {2}, pages = {1683--1709}, doi = {10.3390/sym2031683}, } @Article{KuPa12, author = {Kuptsov, P. V. and Parlitz, U.}, title = {Theory and computation of {Covariant {Lyapunov} Vectors}}, journal = {J. Nonlin. Sci.}, year = {2012}, volume = {22}, pages = {727--762}, doi = {10.1007/s00332-012-9126-5}, } @Article{ShSmRa10, author = {J. A. Sherratt and M. J. Smith and J. D. M. Rademacher}, title = {Patterns of sources and sinks in the complex {Ginzburg-Landau} equation with zero linear dispersion}, journal = {SIAM J. Appl. Dyn. Syst.}, year = {2010}, volume = {9}, pages = {883--918}, doi = {10.1137/090780961}, } @Article{ManBar96, author = {Mantel, R.-M. and Barkley, D.}, title = {Periodic forcing of spiral waves in excitable media}, journal = {Phys. Rev. E}, year = {1996}, volume = {54}, pages = {4791--4802}, doi = {10.1103/PhysRevE.54.4791}, } @Article{PSHMR14, author = {Pecora, L. M. and Sorrentino, F. and Hagerstrom, A. M. and Murphy, T. E. and Roy, R.}, journal = {Nature Commun.}, title = {Cluster synchronization and isolated desynchronization in complex networks with symmetries}, year = {2014}, volume = {5}, doi = {10.1038/ncomms5079}, } @Article{Mayer, author = {D. H. Mayer}, title = {On the thermodynamic formalism for the {Gauss} map}, journal = {Commun. Math. Phys.}, year = {1990}, volume = {130}, pages = {311--333}, doi = {10.1007/bf02473355}, } @Article{Bogomolny1993, author = {E. B. Bogomolny and M. Carioli}, title = {Quantum maps from transfer operators}, journal = {Physica D}, year = {1993}, volume = {67}, pages = {88--112}, doi = {10.1016/0167-2789(93)90199-b}, } @InCollection{Mayer92, author = {D. Mayer}, title = {Thermodynamic formalism and quantum mechanics on the modular surface}, booktitle = {{From Phase Transitions to Chaos}}, publisher = {World Scientific}, year = {1992}, pages = {521--529}, address = {Singapore}, doi = {10.1142/9789814355872_0039}, } @InCollection{Sullivan, author = {Sullivan, D.}, booktitle = {{Universality in Chaos}}, publisher = {Adam Hilger}, title = {Bounded structure of infinitely renormalizable mappings}, year = {1989}, address = {Bristol}, edition = {2}, editor = {P. Cvitanovi{\'c}}, doi = {10.1201/9780203734636}, } @Article{AntOtt81, author = {Antonsen, T. M. and Ott, E.}, title = {Diffusion coefficient for ions in the presence of a coherent lower hybrid wave}, journal = {Phys. Fluids}, year = {1981}, volume = {24}, pages = {1635}, doi = {10.1063/1.863586}, } @Misc{Fefferman2000, author = {Fefferman, C. L.}, title = {Existence and smoothness of the {Navier-Stokes} equation}, year = {2000}, journal = {The Millennium Prize Problems}, pages = {1--6}, url = {http://www.claymath.org/millennium-problems/navier%E2%80%93stokes-equation}, } @InCollection{CBflows, author = {Mainieri, R. and Cvitanovi{\'c}, P. and Spiegel, E. A.}, title = {Go with the flow}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2020}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/paper.shtml#flows}, } @Article{AnBrCi17, author = {A. Anu{\v{s}}i{\'{c}} and H. Bruin and J. {\v{C}}in{\v{c}}}, journal = {Discrete Contin. Dyn. Syst.}, title = {Uncountably many planar embeddings of unimodal inverse limit spaces}, year = {2017}, pages = {2285--2300}, volume = {37}, doi = {10.3934/dcds.2017100}, eprint = {1603.03887}, eprinttype = {arxiv}, } @Misc{LiMaWu17, author = {Liebermann, N. and Main, J. and Wunner, G.}, title = {Exceptional points in the elliptical three-disk scatterer using semiclassical periodic orbit quantization}, year = {2017}, eprint = {1705.00197}, eprinttype = {arxiv}, } @Misc{LiLiao17, author = {X. Li and S. Liao}, title = {One hundred and fifty-two new families of {Newtonian} periodic planar three-body orbits}, year = {2017}, eprint = {1705.00527}, eprinttype = {arxiv}, } @Book{Moiseyev11, author = {Moiseyev, N.}, publisher = {Cambridge Univ. Press}, title = {{Non-Hermitian Quantum Mechanics}}, year = {2011}, address = {Cambridge UK}, doi = {10.1017/cbo9780511976186}, } @Article{Heiss99, author = {W. D. Heiss}, title = {Phases of wave functions and level repulsion}, journal = {Eur. Phys. J. D}, year = {1999}, volume = {7}, pages = {1--4}, doi = {10.1007/s100530050339}, } @Article{Heiss12, author = {W. D. Heiss}, title = {The physics of exceptional points}, journal = {J. Phys. A}, year = {2012}, volume = {45}, pages = {444016}, doi = {10.1088/1751-8113/45/44/444016}, } @Article{Heiss04, author = {W D Heiss}, title = {Exceptional points of non-{Hermitian} operators}, journal = {J. Phys. A}, year = {2004}, volume = {37}, pages = {2455}, doi = {10.1088/0305-4470/37/6/034}, } @Article{MulRot08, author = {M. M{\"u}ller and I. Rotter}, title = {Exceptional points in open quantum systems}, journal = {J. Phys. A}, year = {2008}, volume = {41}, pages = {244018}, doi = {10.1088/1751-8113/41/24/244018}, } @Article{FBCL10, author = {L. Fazendeiro and B.M. Boghosian and P.V. Coveney and J. L{\"a}tt}, title = {Unstable periodic orbits in weak turbulence}, journal = {J. Comput. Sci.}, year = {2010}, volume = {1}, pages = {13--23}, doi = {10.1016/j.jocs.2010.03.004}, } @Article{BBLTFC11, author = {Boghosian, B. M. and Brown, Aa. and L\"att, J. and Tang, H. and Fazendeiro, L. M. and Coveney, P. V.}, title = {Unstable periodic orbits in the {Lorenz} attractor}, journal = {Philos. Trans. Royal Soc. A}, year = {2011}, volume = {369}, pages = {2345--2353}, doi = {10.1098/rsta.2011.0067}, } @Article{BFLTC11, author = {Boghosian, B. M. and Fazendeiro, L. M. and L\"att, J. and Tang, H. and Coveney, P. V.}, title = {New variational principles for locating periodic orbits of differential equations}, journal = {Philos. Trans. Royal Soc. A}, year = {2011}, volume = {369}, pages = {2211--2218}, doi = {10.1098/rsta.2011.0066}, } @Article{FiBoKo05, author = {Finn, L. I. and Boghosian, B. M. and Kottke, C. N.}, title = {Vortex core identification in viscous hydrodynamics}, journal = {Philos. Trans. Royal Soc. A}, year = {2005}, volume = {363}, pages = {1937--1948}, doi = {10.1098/rsta.2005.1620}, } @Article{SmiBog11, author = {Smith, S. A. and Boghosian, B. M.}, journal = {Phys. Rev. E}, title = {Robust numerical method for integration of point-vortex trajectories in two dimensions}, year = {2011}, pages = {056702}, volume = {83}, doi = {10.1103/PhysRevE.83.056702}, } @Article{BALL92, author = {D. Biswas and M. Azam and Q. V. Lawande and S. V Lawande}, title = {Existence of stable periodic orbits in the {$x^2 y^2$} potential: a semiclassical approach}, journal = {J. Phys. A}, year = {1992}, volume = {25}, pages = {L297}, doi = {10.1088/0305-4470/25/7/003}, } @Article{NTOD92, author = {M. L. A. Nip and J. A. Tuszynski and M. Otwinowski and J. M. Dixon}, title = {Search for regular orbits in the {$x^2 y^2$} potential problem}, journal = {J. Phys. A}, year = {1992}, volume = {25}, pages = {5553--5562}, doi = {10.1088/0305-4470/25/21/014}, } @Techreport{Baldr06, author = {K. Baldridge}, title = {{UCSD Chemistry 185/285 course}}, institution = {U. of California, San Diego, La Jolla}, year = {2006}, url = {http://www.sdsc.edu/~kimb/ClassNotes185.html}, } @Article{Frob1896a, author = {Frobenius, G.}, title = {{{{\"U}}ber Beziehungen zwischen den Primidealen eines algebraischen K{\"o}rpers und den Substitutionen seiner Gruppe}}, journal = {S'ber. Akad. d. Wiss. Berlin}, year = {1896}, pages = {689--703}, } @Article{Hawkins1974, author = {Hawkins, T.}, title = {New light on {Frobenius}' creation of the theory of group characters}, journal = {Arch. Hist. Exact Sci.}, year = {1974}, volume = {12}, pages = {217--243}, doi = {10.1007/BF00357245}, } @Article{Frob1896, author = {Frobenius, G.}, title = {{{{\"U}}ber Gruppencharaktere}}, journal = {S'ber. Akad. d. Wiss. Berlin}, year = {1896}, pages = {985-1021}, } @Article{Neimark59, author = {Neimark, J.}, journal = {Dokl. Akad. Nauk SSSR}, title = {On some cases of periodic motions depending on parameters}, year = {1959}, note = {In Russian}, pages = {736--739}, volume = {129}, } @Article{Sacker65, author = {Sacker, R. J.}, title = {A new approach to the perturbation theory of invariant surfaces}, journal = {Commun. Pure Appl. Math.}, year = {1965}, volume = {18}, pages = {717--732}, doi = {10.1002/cpa.3160180409}, } @Article{Bassein98, author = {S. Bassein}, title = {The dynamics of a family of one-dimensional maps}, journal = {Amer. Math. Monthly}, year = {1998}, volume = {105}, pages = {118--130}, doi = {10.2307/2589643}, } @InCollection{ChaosBookChaDiaSch, author = {Chandre, C. and Diakonos, F. K. and Schmelcher, P.}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Institute}, title = {Discrete iteration relaxation method}, year = {2012}, editor = {P. Cvitanovi\'c and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, url = {http://ChaosBook.org/paper.shtml#relax}, } @Incollection{CBook:projects, author = {P. Cvitanovi{\'c}}, title = {Appendix: {Projects}}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2017}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/paper.shtml#projects}, } @InCollection{CBtrace, author = {P. Cvitanovi{\'c}}, title = {Trace formulas}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2020}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/paper.shtml#trace}, } @Incollection{CBook:appendSymm, author = {A. Wirzba and P. Cvitanovi{\'c}}, title = {Appendix: {Discrete} symmetries of dynamics}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2016}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/paper.shtml#appendSymm}, } @InCollection{CBsymm, author = {P. Cvitanovi{\'c}}, title = {Discrete symmetry factorization}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2020}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/paper.shtml#symm}, } @Book{PCgr, author = {Cvitanovi{\'c}, P.}, publisher = {Princeton Univ. Press}, title = {{Group Theory: Birdtracks, Lie's and Exceptional Groups}}, year = {2008}, address = {Princeton NJ}, doi = {10.1515/9781400837670}, } @Article{StrMag77, author = {Strutinskii, V. M. and Magner A. G.}, title = {Quasiclassical theory of the nuclear shell structure}, journal = {Sov. J. Phys. Part. Nucl.}, year = {1977}, volume = {7}, pages = {138--163}, } @Book{BraBha03, title = {{Semiclassical Physics}}, publisher = {Westview Press}, year = {2003}, author = {Brack, M. and Bhaduri, R.K.}, address = {Boulder, CO}, isbn = {9780813340845}, } @Article{Strutinskii75, author = {Strutinskii, V. M.}, title = {Semi-classical theory of nuclear shell structure}, journal = {Nukleonika}, year = {1975}, volume = {20}, pages = {679--716}, } @Article{ChencinerLink, author = {A. Chenciner}, title = {Three body problem}, journal = {Scholarpedia}, year = {2007}, volume = {2}, pages = {2111}, doi = {10.4249/scholarpedia.2111}, } @Article{SoUPOs, author = {P. So}, title = {Unstable periodic orbits}, journal = {Scholarpedia}, year = {2007}, volume = {2}, pages = {1353}, doi = {10.4249/scholarpedia.1358}, } @Article{Franel24, author = {Franel, J.}, title = {Les suites de {Farey} et le probl{\'e}me des nombres premiers}, journal = {Nachr. Ges. Wiss. Gottingen, Math.-Phys.}, year = {1924}, volume = {1924}, pages = {198--201}, url = {http://eudml.org/doc/59156}, } @Book{Neville50, author = {E. H. Neville}, publisher = {Cambridge Univ. Press}, title = {{The Farey Series of Order 1025}}, year = {1950}, address = {Cambridge UK}, doi = {10.2307/3610785}, } @Incollection{Lanford87, author = {O. E. Lanford}, title = {Renormalisation analysis of critical circle mapping with general rotation number}, booktitle = {{VIII International Congress on Mathematical Physics}}, publisher = {World Scientific}, year = {1987}, editor = {Mebkhout, M. and S{\'e}n{\'e}or, R.}, pages = {532--536}, address = {Singapore}, isbn = {9789971502089}, } @Book{MebSen87, title = {{VIII International Congress on Mathematical Physics}}, publisher = {World Scientific}, year = {1987}, author = {Mebkhout, M. and S{\'e}n{\'e}or, R.}, address = {Singapore}, isbn = {9789971502089}, } @Article{HenLipCvi15, author = {J. M. Heninger and D. Lippolis and P. Cvitanovi\'c}, title = {Perturbation theory for the {Fokker-Planck} operator in chaos}, journal = {Commun. Nonlinear Sci. Numer. Simul.}, year = {2018}, volume = {55}, pages = {16--28}, doi = {10.1016/j.cnsns.2017.06.025}, } @Article{GasAlo93, author = {Gaspard, P. and Alonso, D.}, title = {{$\hbar$} expansion for the periodic-orbit quantization of hyperbolic systems}, journal = {Phys. Rev. A}, year = {1993}, volume = {47}, pages = {R3468--R3471}, doi = {10.1103/PhysRevA.47.R3468}, } @Book{Griffiths17, author = {Griffiths, D. J.}, publisher = {Cambridge Univ. Press}, title = {{Introduction to Quantum Mechanics}}, year = {2018}, address = {Cambridge UK}, edition = {3}, doi = {10.1017/9781316995433}, } @Incollection{Perciv77, author = {I. Percival}, title = {Semiclassical theory of bound states}, booktitle = {{Advances in Chemical Physics}}, publisher = {Wiley}, year = {1982}, editor = {I. Prigogine and S. A. Rice}, address = {New York}, doi = {10.1002/9780470142554.ch1}, isbn = {9780471022749}, } @Book{ChaLub95, author = {Chaikin, P. M. and Lubensky, T. C.}, publisher = {Cambridge Univ. Press}, title = {{Principles of Condensed Matter Physics}}, year = {1995}, address = {Cambridge UK}, doi = {10.1017/cbo9780511813467}, } @Book{FieldThe, title = {{Field Theory}}, publisher = {Nordita}, year = {1983}, author = {P. Cvitanovi{\'c}}, address = {Copenhagen}, note = {Notes prepared by E. Gyldenkerne}, url = {http://ChaosBook.org/FieldTheory}, } @Book{Dingle73, title = {{Asymptotic Expansions: Their Derivation and Interpretation}}, publisher = {Academic Press}, year = {1973}, author = {Dingle, R. B.}, isbn = {9780122165504}, address = {London}, doi = {10.2307/2005758}, } @Article{Cvit77b, author = {Cvitanovi{\'c}, P.}, title = {Asymptotic estimates and gauge invariance}, journal = {Nucl. Phys. {B}}, year = {1977}, volume = {127}, pages = {176--188}, doi = {10.1016/0550-3213(77)90357-1}, } @Incollection{CBook:appendLyapunov, author = {P. Cvitanovi{\'c} and G. Vattay}, title = {Appendix: {Transport of vector fields}}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2011}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/paper.shtml#appendLyapunov}, } @Article{brjuno71, author = {A.D. Brjuno}, journal = {Trans. Moscow Math. Soc.}, title = {The analytic form of differential equations}, year = {1971}, pages = {131--288}, volume = {25}, } @Article{brjuno72, author = {A.D. Brjuno}, journal = {Trans. Moscow Math. Soc.}, title = {The analytic form of differential equations}, year = {1972}, pages = {199--238}, volume = {26}, } @Article{VandenBr89, author = {C. Van den Broeck}, title = {Renormalization of first-passage times for random walks on deterministic fractals}, journal = {Phys. Rev. A}, year = {1989}, volume = {40}, pages = {7334}, doi = {10.1103/physreva.40.7334}, } @Misc{CO94, author = {P. Cvitanovi\'c and E. Ott}, title = {Steady fast kinematic dynamos: {The} topological entropy bound and the effect of magnetic field diffusion}, year = {1994}, note = {In preparation}, } @Proceedings{DamHu, title = {{Probabilistic Methods in Quantum Field Theory and Quantum Gravity}}, year = {1990}, editor = {H. H. Damgaard and A. Rosenblum}, volume = {224}, series = {NATO ASI series. Series B, Physics}, address = {New York}, publisher = {Plenum Press}, } @Incollection{gasp_hbar, author = {P. Gaspard}, title = {{$\hbar$}-expansion for quantum trace formulas}, booktitle = {{Quantum Chaos between Order and Disorder}}, publisher = {Cambridge Univ. Press}, year = {1995}, editor = {G. Casati and B. Chirikov}, pages = {385--404}, address = {Cambridge UK}, doi = {10.1017/cbo9780511599989.023}, } @Article{alonso2, author = {D. Alonso and P. Gaspard}, journal = {Chaos}, title = {{$\hbar$} expansion for the periodic-orbit quantization of chaotic systems}, year = {1993}, pages = {601--612}, volume = {3}, doi = {10.1063/1.165964}, } @Article{Nelson75, author = {D. R. Nelson and M. E. Fisher}, journal = {Ann. Phys.}, title = {Soluble renormalization groups and scaling fields for low-dimensional {Ising} systems}, year = {1975}, pages = {226--274}, volume = {91}, doi = {10.1016/0003-4916(75)90284-5}, } @Article{ParWu81, author = {Parisi, G. and Wu, Y. S.}, journal = {Scientia Sinica}, title = {Perturbation-theory without gauge fixing}, year = {1981}, pages = {483--496}, volume = {24}, } @Article{Vattay96, author = {G. Vattay}, journal = {Phys. Rev. Lett.}, title = {{Bohr-Sommerfeld} quantization of periodic orbits}, year = {1996}, pages = {1059--1062}, volume = {76}, doi = {10.1103/physrevlett.76.1059}, } @Misc{Vattay94, author = {G. Vattay}, title = {Differential equations to compute {$\hbar$} corrections of the trace formula}, year = {1994}, eprint = {chao-dyn/9406005}, eprintclass = {chao-dyn}, eprinttype = {arxiv}, } @Incollection{CBvattayNoise, author = {G. Vattay}, title = {Noise and quantum corrections to trace formulas}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {1997}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/paper.shtml#trace}, } @Article{VatRos96, author = {G. Vattay and P. E. Rosenqvist}, title = {Periodic orbit quantization beyond the semiclassical theory}, journal = {Phys. Rev. Lett.}, year = {1996}, volume = {76}, pages = {335--338}, doi = {10.1103/PhysRevLett.76.335}, } @Article{Zheng91a, author = {W.-M. Zheng}, title = {Symbolic dynamics for the {Lozi} map}, journal = {Chaos Solit. Fract.}, year = {1991}, volume = {1}, pages = {243--248}, doi = {10.1016/0960-0779(91)90034-7}, } @Article{FanHao96, author = {H.-P. Fang and B.-L. Hao}, title = {Symbolic dynamics of the {Lorenz} equations}, journal = {Chaos Solit. Fract.}, year = {1996}, volume = {7}, pages = {217--246}, doi = {10.1016/0960-0779(95)00046-1}, } @Article{MicPhi97, author = {Michielin, O. and Phillipson, P. E.}, title = {Map dynamics study of the {Lorenz} equations}, journal = {Int. J. Bifur. Chaos}, year = {1997}, volume = {7}, pages = {373--382}, doi = {10.1142/S0218127497000248}, } @Article{Sonis96, author = {M. Sonis}, title = {Once more on {H{\'e}non} map: {Analysis} of bifurcations}, journal = {Chaos Solit. Fract.}, year = {1996}, volume = {7}, pages = {2215--2234}, doi = {10.1016/S0960-0779(96)00081-1}, } @Article{OlWuKi17, author = {Olyaei, A. A. and Wu, C. and Ki, W.}, title = {Detecting unstable periodic orbits in chaotic time series using synchronization}, journal = {Phys. Rev. E}, year = {2017}, volume = {96}, pages = {012207}, doi = {10.1103/PhysRevE.96.012207}, } @Article{LiTom17, author = {Li, J. and Tomsovic, S.}, title = {Geometric determination of classical actions of heteroclinic and unstable periodic orbits}, journal = {Phys. Rev. E}, year = {2017}, volume = {95}, pages = {062224}, doi = {10.1103/PhysRevE.95.062224}, } @Article{LiTom17a, author = {Li, J. and Tomsovic, S.}, title = {Accurate determination of heteroclinic orbits in chaotic dynamical systems}, journal = {J. Phys. A}, year = {2017}, volume = {50}, pages = {135101}, doi = {10.1088/1751-8121/aa5fe6}, } @Article{BevBas00, author = {Bevilaqua, D.V. and Bas{\'i}lio De Matos, M.}, title = {Universal pattern for homoclinic and periodic points}, journal = {Physica D}, year = {2000}, volume = {145}, pages = {13--24}, doi = {10.1016/S0167-2789(00)00088-9}, } @Article{Kac66, author = {M. Kac}, title = {Can one hear the shape of a drum?}, journal = {Amer. Math. Monthly}, year = {1966}, volume = {73}, pages = {1--23}, url = {http://www.jstor.org/stable/2313748}, } @PhdThesis{LippolisThesis, author = {Lippolis, D.}, title = {{How well can one resolve the state space of a chaotic map?}}, school = {School of Physics, Georgia Inst. of Technology}, year = {2010}, address = {Atlanta}, url = {http://ChaosBook.org/projects/theses.html}, } @Article{GioCer05, author = {M. Giona and S. Cerbelli}, title = {Connecting the spatial structure of periodic orbits and invariant manifolds in hyperbolic area-preserving systems}, journal = {Phys. Lett. A}, year = {2005}, volume = {347}, pages = {200--207}, doi = {10.1016/j.physleta.2005.08.005}, } @Article{BuKe07, author = {Kennel, M. B. and Buhl, M.}, title = {Globally enumerating unstable periodic orbits for observed data using symbolic dynamics}, journal = {Chaos}, year = {2007}, volume = {17}, pages = {033102}, doi = {10.1063/1.2743099}, } @Article{BuKe03, author = {Kennel, M. B. and Buhl, M.}, title = {Estimating good discrete partitions from observed data: {Symbolic} false nearest neighbors}, journal = {Phys. Rev. Lett.}, year = {2003}, volume = {91}, pages = {084102}, doi = {10.1063/1.1612266}, } @InProceedings{BuKe03a, author = {Kennel, M. B. and Buhl, M.}, title = {Estimating good discrete partitions from observed data: symbolic false nearest neighbors}, booktitle = {{Experimental Chaos: Seventh Experimental Chaos Conference}}, year = {2003}, editor = {Ko\v{c}arev, L. and Carroll, T. L. and Gluckman, B. J. and Boccaletti, S. and Kurths, J.}, pages = {380--380}, address = {Melville, NY}, publisher = {American Institute of Physics}, doi = {10.1063/1.1612266}, } @Article{BuKe05, author = {{Buhl}, M. and {Kennel}, M.~B.}, title = {Statistically relaxing to generating partitions for observed time-series data}, journal = {Phys. Rev. E}, year = {2005}, volume = {71}, pages = {046213}, doi = {10.1103/PhysRevE.71.046213}, } @Article{MR94, author = {G. P. Morriss and L. Rondoni}, title = {Periodic orbit expansions for the {Lorentz} gas}, journal = {J. Stat. Phys.}, year = {1994}, volume = {75}, pages = {553--584}, doi = {10.1007/BF02186872}, } @Article{ViSa09, author = {Viswanath, D. and {\c{S}}ahuto{\u{g}}lu, S.}, title = {Complex singularities and the {Lorenz} attractor}, journal = {SIAM Rev.}, year = {2010}, volume = {52}, pages = {294--314}, doi = {10.1137/090753474}, } @Article{DV01, author = {D. Viswanath}, title = {Global errors of numerical {ODE} solvers and {Lyapunov}'s theory of stability}, journal = {IMA J. Numer. Anal.}, year = {2001}, volume = {21}, pages = {387--406}, doi = {10.1093/imanum/21.1.387}, } @Article{DetDah98, author = {Dettmann, C. P. and Dahlqvist, P.}, title = {Computing the diffusion coefficient for intermittent maps: {Resummation} of stability ordered cycle expansions}, journal = {Phys. Rev. E}, year = {1998}, volume = {57}, pages = {5303--5310}, doi = {10.1103/PhysRevE.57.5303}, } @Article{dahlqvist1997decay, author = {Dahlqvist, P.}, journal = {J. Technical Phys.}, title = {Decay of correlations, {Lyapunov} exponents and anomalous diffusion in the {Sinai} billiard}, year = {1997}, pages = {189--194}, volume = {38}, eprint = {chao-dyn/9510020}, eprintclass = {chao-dyn}, eprinttype = {arxiv}, } @Article{Dettmann99, author = {Dettmann, C. P.}, title = {Traces and determinants of strongly stochastic operators}, journal = {Phys. Rev. E}, year = {1999}, volume = {59}, pages = {5231--5234}, doi = {10.1103/PhysRevE.59.5231}, } @Article{Sakhr01, author = {Sakhr, J.}, title = {Amplitude ordering of the trace formula for the two-particle disk billiard}, journal = {Phys. Rev. A}, year = {2001}, volume = {64}, pages = {044102}, doi = {10.1103/PhysRevA.64.044102}, } @Article{Dahlqvist96, author = {Dahlqvist, P.}, title = {Lyapunov exponents and anomalous diffusion of a {Lorentz} gas with infinite horizon using approximate zeta functions}, journal = {J. Stat. Phys.}, year = {1996}, volume = {84}, pages = {773--795}, doi = {10.1007/BF02179657}, } @Article{DahArt96, author = {P. Dahlqvist and . Artuso}, title = {On the decay of correlations in {Sinai} billiards with infinite horizon}, journal = {Phys. Lett. A}, year = {1996}, volume = {219}, pages = {212--216}, doi = {10.1016/0375-9601(96)00404-5}, } @Article{BorGrz06, author = {P. Borys and Z. J. Grzywna}, title = {Diffusion as a result of transition in behavior of deterministic maps}, journal = {Chaos Solit. Fract.}, year = {2006}, volume = {30}, pages = {156--165}, doi = {10.1016/j.chaos.2005.08.163}, } @Article{Dahlqvist97, author = {P. Dahlqvist}, title = {The {Lyapunov} exponent in the {Sinai} billiard in the small scatterer limit}, journal = {Nonlinearity}, year = {1997}, volume = {10}, pages = {159}, doi = {10.1088/0951-7715/10/1/011}, } @Article{Artuso97, author = {R. Artuso}, title = {Anomalous diffusion in classical dynamical systems}, journal = {Phys. Rep.}, year = {1997}, volume = {290}, pages = {37--47}, doi = {10.1016/S0370-1573(97)00057-4}, } @Article{Dahlqvist99, author = {P. Dahlqvist}, title = {Error of semiclassical eigenvalues in the semiclassical limit - an asymptotic analysis of the {Sinai} billiard}, journal = {J. Phys. A}, year = {1999}, volume = {32}, pages = {7317}, doi = {10.1088/0305-4470/32/42/307}, } @Article{Dahlqvist97a, author = {P. Dahlqvist}, title = {The role of singularities in chaotic spectroscopy}, journal = {Chaos Solit. Fract.}, year = {1997}, volume = {8}, pages = {1011--1029}, doi = {10.1016/S0960-0779(97)00006-4}, } @Article{DahVat98, author = {P. Dahlqvist and G. Vattay}, title = {Periodic orbit quantization of the {Sinai} billiard in the small scatterer limit}, journal = {J. Phys. A}, year = {1998}, volume = {31}, pages = {6333}, doi = {10.1088/0305-4470/31/30/003}, } @Article{Dahlqvist99a, author = {P. Dahlqvist}, title = {From chaotic to disordered systems - a periodic orbit approach}, journal = {J. Phys. A}, year = {1999}, volume = {32}, pages = {725}, url = {http://stacks.iop.org/0305-4470/32/i=5/a=005}, } @Article{ArHuOt03, author = {Armstead, D. N. and Hunt, B. R. and Ott, E.}, title = {Anomalous diffusion in infinite horizon billiards}, journal = {Phys. Rev. E}, year = {2003}, volume = {67}, pages = {021110}, doi = {10.1103/PhysRevE.67.021110}, } @Article{CGLS14, author = {Cristadoro, G. and Gilbert, T. and Lenci, M. and Sanders, D. P.}, title = {Measuring logarithmic corrections to normal diffusion in infinite-horizon billiards}, journal = {Phys. Rev. E}, year = {2014}, volume = {90}, pages = {022106}, doi = {10.1103/PhysRevE.90.022106}, } @Article{CGLS14a, author = {Cristadoro, G. and Gilbert, T. and Lenci, M. and Sanders, D. P.}, title = {{Machta-Zwanzig} regime of anomalous diffusion in infinite-horizon billiards}, journal = {Phys. Rev. E}, year = {2014}, volume = {90}, pages = {050102}, doi = {10.1103/PhysRevE.90.050102}, } @Article{CGMR15, author = {F. Cagnetta and G. Gonnella and A. Mossa and S. Ruffo}, title = {Strong anomalous diffusion of the phase of a chaotic pendulum}, journal = {Europhys. Lett.}, year = {2015}, volume = {111}, pages = {10002}, doi = {10.1209/0295-5075/111/10002}, } @Article{RDHB14, author = {Rebenshtok, A. and Denisov, S. and H\"anggi, P. and Barkai, E.}, title = {Non-normalizable densities in strong anomalous diffusion: beyond the central limit theorem}, journal = {Phys. Rev. Lett.}, year = {2014}, volume = {112}, pages = {110601}, doi = {10.1103/PhysRevLett.112.110601}, } @Article{ArtCri05, author = {R. Artuso and G. Cristadoro}, title = {Anomalous deterministic transport}, journal = {Chaos}, year = {2005}, volume = {15}, pages = {015116}, doi = {10.1063/1.1832811}, } @Article{ArtCri03a, author = {R. Artuso and G. Cristadoro}, title = {Anomalous transport: {A} deterministic approach}, journal = {Phys. Rev. Lett.}, year = {2003}, volume = {90}, pages = {244101}, doi = {10.1103/PhysRevLett.90.244101}, } @Article{Artuso2008, author = {Artuso, R. and Cavallasca, L. and Cristadoro, G.}, title = {Dynamical and transport properties in a family of intermittent area-preserving maps}, journal = {Phys. Rev. E}, year = {2008}, volume = {77}, pages = {046206}, doi = {10.1103/PhysRevE.77.046206}, } @Article{ArtCri04, author = {Artuso, R. and Cristadoro, G.}, journal = {J. Phys. A}, title = {Periodic orbit theory of strongly anomalous transport}, year = {2004}, pages = {85--103}, volume = {37}, doi = {10.1088/0305-4470/37/1/006}, } @Misc{DahNie98, author = {Dahlqvist, P. and Nielsen, S. F.}, title = {Periodic orbit theory for angle diffusion in the closed 3 disk billiard}, year = {1998}, url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.4220}, } @Book{Goldenfeld92, title = {{Lectures on Phase Transitions and the Renormalization Group}}, publisher = {Westview Press}, year = {1992}, author = {Goldenfeld, N.}, isbn = {9780201554090}, } @Book{Kardar07, author = {Kardar, M.}, publisher = {Cambridge Univ. Press}, title = {{Statistical Physics of Fields}}, year = {2007}, address = {Cambridge UK}, doi = {10.1017/cbo9780511815881}, } @Article{Dehaye05, author = {Dehaye, P.-O.}, title = {Averages over classical {Lie} groups, twisted by characters}, journal = {J. Combin. Theory A}, year = {2007}, volume = {114}, pages = {1278 - 1292}, doi = {10.1016/j.jcta.2007.01.008}, } @Book{Kadanoff00, title = {{Statistical Physics: Statics, Dynamics and Renormalization}}, publisher = {World Scientific}, year = {2000}, author = {Kadanoff, L. P.}, address = {Singapore}, doi = {10.1142/4016}, } @Article{JuMWuHe17, author = {Junginger, A. and Main, J. and Wunner, G. and Hernandez, R.}, title = {Variational principle for the determination of unstable periodic orbits and instanton trajectories at saddle points}, journal = {Phys. Rev. A}, year = {2017}, volume = {95}, pages = {032130}, doi = {10.1103/PhysRevA.95.032130}, } @Article{JimMan09, author = {Jim{\'e}nez Madrid, J. A. and Mancho, A. M.}, title = {Distinguished trajectories in time dependent vector fields}, journal = {Chaos}, year = {2009}, volume = {19}, pages = {013111}, doi = {10.1063/1.3056050}, } @Article{MaLiLa13, author = {Ma, H. and Lin, W. and Lai, Y.-.}, title = {Detecting unstable periodic orbits in high-dimensional chaotic systems from time series: {Reconstruction} meeting with adaptation}, journal = {Phys. Rev. E}, year = {2013}, volume = {87}, pages = {050901}, doi = {10.1103/PhysRevE.87.050901}, } @Article{MaHoLaLi15, author = {Ma, H. and Ho, D. W. C. and Lai, Y.-C. and Lin, W.}, title = {Detection meeting control: {Unstable} steady states in high-dimensional nonlinear dynamical systems}, journal = {Phys. Rev. E}, year = {2015}, volume = {92}, pages = {042902}, doi = {10.1103/PhysRevE.92.042902}, } @Article{Mathew07, author = {Mathew, G. and Mezi{\'c}, I. and Grivopoulos, S. and Vaidya, U. and Petzold, L.}, title = {Optimal control of mixing in {Stokes} fluid flows}, journal = {J. Fluid Mech.}, year = {2007}, volume = {580}, pages = {261--281}, doi = {10.1017/s0022112007005332}, } @Book{maslov72, title = {{Th{\'e}orie des perturbations et m{\'e}thodes asymptotiques}}, publisher = {Dunod}, year = {1972}, author = {Maslov, V. P.}, isbn = {9782040082512}, } @Article{Arnold67maslov, author = {Arnol'd, V. I.}, title = {Characteristic class entering in quantization conditions}, journal = {Funct. Anal. Appl.}, year = {1967}, volume = {1}, pages = {1--13}, doi = {10.1007/BF01075861}, } @Book{Lorenz95, author = {Lorenz, E. N.}, publisher = {Taylor \& Francis}, title = {{The Essence Of Chaos}}, year = {1995}, doi = {10.4324/9780203214589}, } @Article{WegSol02, author = {Wegman, E. J. and Solka, J. L.}, title = {On some mathematics for visualizing high dimensional data}, journal = {Sankhya: Indian J. Statistics, Ser. A}, year = {2002}, volume = {64}, pages = {429--452}, url = {http://www.jstor.org/stable/25051404}, } @Article{SeiSta16, author = {E. Seiler and Stamatescu, I. O.}, title = {A note on the loop formula for the fermionic determinant}, journal = {J. Phys. A}, year = {2016}, volume = {49}, pages = {335401}, doi = {10.1088/1751-8113/49/33/335401}, } @Article{Pomeau95, author = {Y. Pomeau}, journal = {Chaos Solit. Fract.}, title = {Remarks on bifurcations with symmetry}, year = {1995}, pages = {1755--1761}, volume = {5}, doi = {10.1016/0960-0779(94)00174-O}, } @Article{Faraz15, author = {Farazmand, M.}, title = {An adjoint-based approach for finding invariant solutions of {Navier-Stokes} equations}, journal = {J. Fluid Mech.}, year = {2016}, volume = {795}, pages = {278--312}, doi = {10.1017/jfm.2016.203}, } @Book{OlvSha06, author = {Olver, P. J. and Shakiban, C.}, publisher = {Prentice-Hall}, title = {{Applied Linear Algebra}}, year = {2006}, address = {Upper Saddle River, NJ}, doi = {10.1007/978-3-319-91041-3}, } @Book{Steeb16, title = {{Problems and Solutions: Nonlinear Dynamics, Chaos and Fractals}}, publisher = {World Scientific}, year = {2016}, author = {Steeb, W.H.}, isbn = {9789813109940}, doi = {10.1142/10041}, } @Article{Lecian13, author = {Lecian, O. M.}, title = {Reflections on the hyperbolic plane}, journal = {Int. J. Mod. Phys. D}, year = {2013}, volume = {22}, pages = {1350085}, doi = {10.1142/S0218271813500855}, } @Article{Ballou12, author = {Ballou, R.}, title = {An introduction to the linear representations of finite groups}, journal = {EPJ Web Conf.}, year = {2012}, volume = {22}, pages = {00005}, doi = {10.1051/epjconf/20122200005}, } @Article{CanSch12, author = {Canals, B. and Schober, H.}, title = {Introduction to group theory}, journal = {EPJ Web Conf.}, year = {2012}, volume = {22}, pages = {00004}, doi = {10.1051/epjconf/20122200004}, } @Article{GreBal12, author = {Grenier, B. and Ballou, R.}, title = {Crystallography: {Symmetry} groups and group representations}, journal = {EPJ Web Conf.}, year = {2012}, volume = {22}, pages = {00006}, doi = {10.1051/epjconf/20122200006}, } @Article{RodBou12, author = {Rodr{\'i}guez-Carvajal, J. and Bour{\'e}e, F.}, title = {Symmetry and magnetic structures}, journal = {EPJ Web Conf.}, year = {2012}, volume = {22}, pages = {00010}, doi = {10.1051/epjconf/20122200010}, } @Article{Schweizer12, author = {Schweizer, J.}, title = {Conjugation and co-representation analysis of magnetic structures}, journal = {EPJ Web Conf.}, year = {2012}, volume = {22}, pages = {00011}, doi = {10.1051/epjconf/20122200011}, keywords = {very nice black white gray groups}, } @Article{Villain12, author = {Villain, J.}, title = {Symmetry and group theory throughout physics}, journal = {EPJ Web Conf.}, year = {2012}, volume = {22}, pages = {00002}, doi = {10.1051/epjconf/20122200002}, } @Article{Schober12, author = {Schober, H.}, title = {Symmetry characterization of electrons and lattice excitations}, journal = {EPJ Web Conf.}, year = {2012}, volume = {22}, pages = {00012}, doi = {10.1051/epjconf/20122200012}, } @Book{Landau70, author = {L. D. Landau and E. M. Lifshitz}, publisher = {Pergamon Press}, title = {{Theory of Elasticity}}, year = {1970}, address = {Oxford}, edition = {3}, isbn = {9780080570693}, url = {https://archive.org/details/TheoryOfElasticity}, } @Article{Adler98, author = {Adler, R. L.}, title = {Symbolic dynamics and {Markov} partitions}, journal = {Bull. Amer. Math. Soc.}, year = {1998}, volume = {35}, pages = {1--56}, doi = {10.1090/S0273-0979-98-00737-X}, } @Article{Hadamard98, author = {Hadamard, J. S.}, journal = {J. Math. Pures Appl.}, title = {Les surfaces {\`a} courbures oppos{\'e}es et leurs lignes g{\'e}od{\'e}sique}, year = {1898}, pages = {27--73}, volume = {4}, url = {http://sites.mathdoc.fr/JMPA/PDF/JMPA_1898_5_4_A3_0.pdf}, } @Article{BoVuHe78, author = {I. B. Bo{\v{z}}ovi{\'c} and M. Vuji{\v{c}}i{\'c} and F. Herbut}, title = {Irreducible representations of the symmetry groups of polymer molecules. {I}}, journal = {J. Phys. A}, year = {1978}, volume = {11}, pages = {2133}, doi = {10.1088/0305-4470/11/11/003}, } @Article{Bozovic81, author = {I. B. Bo{\v{z}}ovi{\'c}}, title = {Irreducible representations of the symmetry groups of polymer molecules. {III. Consequences} of time-reversal symmetry}, journal = {J. Phys. A}, year = {1981}, volume = {14}, pages = {1825}, doi = {10.1088/0305-4470/14/8/010}, } @Article{Johnston60, author = {D. F. Johnston}, title = {Group theory in solid state physics}, journal = {Rep. Prog. Phys.}, year = {1960}, volume = {23}, pages = {66}, doi = {10.1088/0034-4885/23/1/302}, } @Article{GalCoh95, author = {G. Gallavotti and E. G. D. Cohen}, title = {Dynamical ensembles in nonequilibrium statistical mechanics}, journal = {Phys. Rev. Lett.}, year = {1995}, volume = {74}, pages = {2694--2697}, doi = {10.1103/PhysRevLett.74.2694}, } @Inproceedings{Moffatt90, author = {H. K. Moffatt}, title = {Fixed points of turbulent dynamical systems and suppression of nonlinearity, {Comment} 1}, booktitle = {{Whither Turbulence? Turbulence at the Crossroads}}, year = {1990}, editor = {J. L. Lumley}, pages = {250--257}, address = {New York}, publisher = {Springer}, doi = {10.1007/3-540-52535-1_47}, } @Article{ChLiPfYa17, author = {Charbonneau, P. and Li, Y. and Pfister, H. D. and Yaida, S.}, title = {Cycle-expansion method for the {Lyapunov} exponent, susceptibility, and higher moments}, journal = {Phys. Rev. E}, year = {2017}, volume = {96}, pages = {032129}, doi = {10.1103/PhysRevE.96.032129}, } @Article{GilTho77, author = {Giles, R. and Thorn, C. B.}, title = {Lattice approach to string theory}, journal = {Phys. Rev. D}, year = {1977}, volume = {16}, pages = {366--386}, doi = {10.1103/PhysRevD.16.366}, } @Article{PapTho13, author = {Papathanasiou, G. and Thorn, C. B.}, title = {Worldsheet propagator on the lightcone worldsheet lattice}, journal = {Phys. Rev. D}, year = {2013}, volume = {87}, pages = {066005}, doi = {10.1103/PhysRevD.87.066005}, } @Article{ChuYau00, author = {F. Chung and S.-T. Yau}, title = {Discrete {Green's} functions}, journal = {J. Combin. Theory A}, year = {2000}, volume = {91}, pages = {191--214}, doi = {10.1006/jcta.2000.3094}, } @Article{MiDuWh92, author = {J. W. Mintmire and B. I. Dunlap and C. T. White}, title = {Are {Fullerene} tubules metallic?}, journal = {Phys. Rev. Lett.}, year = {1992}, volume = {68}, pages = {631--634}, doi = {10.1103/physrevlett.68.631}, } @Article{Herring37, author = {Herring, C.}, title = {Effect of time-reversal symmetry on energy bands of crystals}, journal = {Phys. Rev.}, year = {1937}, volume = {52}, pages = {361--365}, doi = {10.1103/PhysRev.52.361}, } @Book{Herzberg50, title = {{Molecular Spectra and Molecular Structure}}, publisher = {Van Nostrand}, year = {1950}, author = {Herzberg, G.}, address = {Princenton NJ}, url = {https://archive.org/details/molecularspectra032774mbp}, } @Book{Kittel96, author = {Kittel, C.}, publisher = {Wiley}, title = {{Introduction to Solid State Physics}}, year = {2004}, edition = {8}, isbn = {9780471415268}, doi = {10.1063/1.3060399}, } @Article{SerRok16, author = {Serkh, K. and Rokhlin, V.}, title = {On the solution of the {Helmholtz} equation on regions with corners}, journal = {Proc. Natl. Acad. Sci. USA}, year = {2016}, volume = {113}, pages = {9171--9176}, doi = {10.1073/pnas.1609578113}, } @Article{Ikeda79, author = {K. Ikeda}, journal = {Opt. Commun.}, title = {Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system}, year = {1979}, pages = {257--261}, volume = {30}, doi = {10.1016/0030-4018(79)90090-7}, } @Inproceedings{dlLlave00, author = {de la Llave, R.}, title = {Variational methods for quasiperiodic solutions of partial differential equations}, booktitle = {{Hamiltonian Systems and Celestial Mechanics (HAMSYS-98)}}, year = {2000}, editor = {Delgado, J. and Lacomba, E. A. and P{\'e}rez-Chavela, E. and Llibre, J.}, isbn = {9789814492119}, address = {Singapore}, publisher = {World Scientific}, doi = {10.1142/4557}, url = {http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=00-56}, } @Book{DLPL00, title = {{Hamiltonian Systems and Celestial Mechanics (HAMSYS-98)}}, publisher = {World Scientific}, year = {2000}, author = {Delgado, J. and Lacomba, E. A. and P{\'e}rez-Chavela, E. and Llibre, J.}, isbn = {9789814492119}, address = {Singapore}, doi = {10.1142/4557}, } @Misc{Grassberger17, author = {P. Grassberger}, title = {Some comments on computational mechanics, complexity measures, and all that}, year = {2017}, url = {https://arXiv.org/abs/1708.03197}, } @Article{Silver17, author = {D. S. Silver}, title = {The new language of mathematics}, journal = {Amer. Sci.}, year = {2017}, volume = {105}, pages = {364}, doi = {10.1511/2017.105.6.364}, } @Article{PetWey27, author = {Peter, F. and Weyl, H.}, title = {{Die Vollst{\"a}ndigkeit der primitiven Darstellungen einer geschlossenen kontinuierlichen Gruppe}}, journal = {Math. Ann.}, year = {1927}, volume = {97}, pages = {737--755}, doi = {10.1007/BF01447892}, } @Inproceedings{HarSeg14, author = {V. Hart and H. Segerman}, title = {The quaternion group as a symmetry group}, booktitle = {{Proc. Bridges 2014: Mathematics, Music, Art, Architecture, Culture}}, year = {2014}, editor = {G. Greenfield, G. Hart and R. Sarhangi}, isbn = {978-1-938664-11-3}, pages = {143--150}, address = {Phoenix, Arizona}, publisher = {Tessellations Publ.}, url = {http://archive.bridgesmathart.org/2014/bridges2014-143.html}, } @Article{WaBrAkGu17, author = {D. Waltner and P. Braun and M. Akila and T. Guhr}, title = {Trace formula for interacting spins}, journal = {J. Phys. A}, year = {2017}, volume = {50}, pages = {085304}, doi = {10.1088/1751-8121/aa5533}, } @Article{Tseng96, author = {H.-C. Tseng and H.-J. Che}, title = {Analytic results for the diffusion coefficient of a piecewise linear map}, journal = {Int. J. Mod. Phys. B}, year = {1996}, volume = {10}, pages = {1913--1934}, doi = {10.1142/S0217979296000878}, } @Article{Chen95, author = {Chen, C.-C.}, title = {Diffusion coefficient of piecewise linear maps}, journal = {Phys. Rev. E}, year = {1995}, volume = {51}, pages = {2815--2822}, doi = {10.1103/PhysRevE.51.2815}, } @Book{Reichl04, author = {Reichl, L.}, publisher = {Springer}, title = {{The Transition to Chaos: Conservative Classical Systems and Quantum Manifestations}}, year = {2004}, address = {New York}, edition = {2}, isbn = {9781475743500}, } @Book{haake01, author = {Haake, F.}, publisher = {Springer}, title = {{Quantum Signatures of Chaos}}, year = {2010}, address = {Berlin}, edition = {3}, doi = {10.1007/978-3-662-04506-0}, } @Article{Schroed26-384, author = {Schr\"odinger, E.}, journal = {Ann. Phys.}, title = {{\"Uber} das {Verh{\"a}ltnis der Heisenberg-Born-Jordanschen Quantenmechanik} zu der meinem}, year = {1926}, pages = {734--756}, volume = {384}, doi = {10.1002/andp.19263840804}, } @Article{Schroed26-I, author = {Schr\"odinger, E.}, title = {{Quantisierung als Eigenwertproblem}}, journal = {Ann. Phys.}, year = {1926}, volume = {384}, pages = {361--376}, doi = {10.1002/andp.19263840404}, } @Article{Schroed26-II, author = {Schr\"odinger, E.}, title = {{Quantisierung als Eigenwertproblem}}, journal = {Ann. Phys.}, year = {1926}, volume = {384}, pages = {489--527}, doi = {10.1002/andp.19263840602}, } @Article{Schroed26-III, author = {Schr\"odinger, E.}, title = {{Quantisierung als Eigenwertproblem}}, journal = {Ann. Phys.}, year = {1926}, volume = {385}, pages = {437--490}, doi = {10.1002/andp.19263851302}, } @Article{Schroed26-IV, author = {Schr\"odinger, E.}, title = {{Quantisierung als Eigenwertproblem}}, journal = {Ann. Phys.}, year = {1926}, volume = {386}, pages = {109--139}, doi = {10.1002/andp.19263861802}, } @Article{Madelung27, author = {Madelung, E.}, title = {Quantentheorie in hydrodynamischer {Form}}, journal = {Z. f. Physik}, year = {1927}, volume = {40}, pages = {322--326}, doi = {10.1007/BF01400372}, } @Article{Bohm52, author = {Bohm, D.}, title = {A suggested interpretation of the quantum theory in terms of ``hidden'' variables. {I}}, journal = {Phys. Rev.}, year = {1952}, volume = {85}, pages = {166--179}, doi = {10.1103/PhysRev.85.166}, } @Article{DV02a, author = {Dieci, L. and Van Vleck, E. S.}, journal = {SIAM J. Numer. Anal.}, title = {{Lyapunov} spectral intervals: {Theory} and computation}, year = {2002}, pages = {516--542}, volume = {40}, doi = {10.1137/s0036142901392304}, } @Article{VanVleck28, author = {Van Vleck, J. H.}, title = {The correspondence principle in the statistical interpretation of quantum mechanics}, journal = {Proc. Natl. Acad. Sci.}, year = {1928}, volume = {14}, pages = {178--188}, doi = {10.1073/pnas.14.2.178}, } @Book{Holland93, author = {Holland, P. R.}, publisher = {Cambridge Univ. Press}, title = {{The Quantum Theory of Motion: An Account of the de Broglie-Bohm Causal Interpretation of Quantum Mechanics}}, year = {1993}, address = {Cambridge UK}, doi = {10.1017/cbo9780511622687}, } @Book{Kline72, title = {{Mathematical Thought from Ancient to Modern Times}}, publisher = {Oxford Univ. Press}, year = {1972}, author = {Kline, M.}, isbn = {9780195061352}, address = {Oxford UK}, doi = {10.2307/3615488}, } @Book{Bell37, title = {{Men of Mathematics}}, publisher = {Penguin}, year = {1937}, author = {Bell, E. T.}, isbn = {9781476784250}, address = {London UK}, doi = {10.2307/3028778}, } @Article{speccolo, author = {E. A. Spiegel}, title = {Stellar convection theory. {I - The} anelastic modal equations}, journal = {Astrophys. J.}, year = {1976}, volume = {207}, pages = {233--243}, doi = {10.1086/154487}, } @Book{Feynman_sp, author = {Feynman, R. P.}, publisher = {{CRC} Press}, title = {{Statistical Mechanics}}, year = {1972}, address = {New York}, doi = {10.1201/9780429493034}, } @Book{Maslov81, title = {{Semi-Classical Approximation in Quantum Mechanics}}, publisher = {Reidel}, year = {1981}, author = {Maslov, V. P. and Fedoriuk, M. V.}, isbn = {978-90-277-1219-6}, address = {Boston}, } @Article{HelTomSep92, author = {Heller, E. J. and Tomsovic, S. and Sep{\'u}lveda, M. A.}, journal = {Chaos}, title = {Time domain approach to semiclassical dynamics: {Breaking} the log time barrier}, year = {1992}, pages = {105-115}, doi = {10.1063/1.165913}, } @Article{Littlejohn92, author = {Littlejohn, Robert G.}, title = {The {Van Vleck} formula, {Maslov} theory, and phase space geometry}, journal = {J. Stat. Phys.}, year = {1992}, volume = {68}, pages = {7--50}, doi = {10.1007/BF01048836}, } @Article{BetUhl37, author = {E. Beth and G. E. Uhlenbeck}, title = {The quantum theory of the non-ideal gas. {II. Behaviour} at low temperatures}, journal = {Physica}, year = {1937}, volume = {4}, pages = {915--924}, doi = {10.1016/S0031-8914(37)80189-5}, } @Book{UFM63, title = {{Lectures in Statistical Mechanics}}, publisher = {Amer. Math. Soc.}, year = {1963}, author = {Uhlenbeck, G. E. and Ford, G. W. and Montroll, E. W.}, url = {http://www.dtic.mil/dtic/tr/fulltext/u2/400926.pdf}, } @Article{MuHeAtBrHa09, author = {S. M{\"u}ller and S. Heusler and A. Altland and P. Braun and F. Haake}, title = {Periodic-orbit theory of universal level correlations in quantum chaos}, journal = {New J. Phys.}, year = {2009}, volume = {11}, pages = {103025}, doi = {10.1088/1367-2630/11/10/103025}, } @Article{Voros88, author = {A. Voros}, title = {Unstable periodic orbits and semiclassical quantisation}, journal = {J. Phys. A}, year = {1988}, volume = {21}, pages = {685}, doi = {10.1088/0305-4470/21/3/023}, } @Article{Voros94, author = {Voros, A.}, title = {Aspects of semiclassical theory in the presence of classical chaos}, journal = {Progr. Theor. Phys. Suppl.}, year = {1994}, volume = {116}, pages = {17--44}, doi = {10.1143/PTP.116.17}, } @Inproceedings{CR93, author = {Cvitanovi{\'c}, P. and Rosenqvist, P. E.}, title = {A new determinant for quantum chaos}, booktitle = {From Classical to Quantum Chaos}, year = {1993}, editor = {G. F. Dell'Antonio, S. Fantoni and V. R. Manfredi}, volume = {41}, pages = {57--64}, address = {Bologna}, organization = {Soc. Italiana di Fisica Conf. Proceed.}, publisher = {Ed. Compositori}, url = {https://arXiv.org/abs/chao-dyn/9304003}, } @Article{Bogomolny92, author = {E. B. Bogomolny}, title = {Semiclassical quantization of multidimensional systems}, journal = {Nonlinearity}, year = {1992}, volume = {5}, pages = {805--866}, doi = {10.1088/0951-7715/5/4/001}, } @Article{Bogomolny92a, author = {E. Bogomolny}, journal = {Chaos}, title = {On dynamical zeta function}, year = {1992}, pages = {5--13}, volume = {2}, doi = {10.1063/1.165898}, } @Article{Friedel52, author = {J. Friedel}, title = {{XIV. The} distribution of electrons round impurities in monovalent metals}, journal = {Phil. Mag.}, year = {1952}, volume = {43}, pages = {153--189}, doi = {10.1080/14786440208561086}, } @Article{Krein53, author = {M. G. Krein}, title = {On the trace formula in perturbation theory}, journal = {Mat. Sb. (N.S.)}, year = {1953}, volume = {33}, pages = {597--626}, url = {http://mi.mathnet.ru/msb5397}, } @Article{Krein62, author = {M. G. Krein}, title = {Perturbation determinants and formula for traces of unitary and self-adjoint operators}, journal = {Sov. Math. Dokl.}, year = {1962}, volume = {3}, pages = {707--710}, } @Article{KreBir62, author = {Krein, M. G. and Birman, M. S.}, title = {On the theory of wave operators and scattering operators}, journal = {Dokl. Akad. Nauk SSSR}, year = {1962}, volume = {144}, pages = {740--744}, } @Article{BirYaf92, author = {Birman, M. S. and Yafaev, D. R.}, journal = {Algebra i Analiz}, title = {The spectral shift function. {The papers of M. G. Krein} and their further development}, year = {1992}, pages = {1--44}, volume = {4}, url = {http://mi.mathnet.ru/eng/aa343}, } @Article{Lloyd67, author = {P. Lloyd}, title = {Wave propagation through an assembly of spheres: {II. The} density of single-particle eigenstates}, journal = {Proc. Phys. Soc.}, year = {1967}, volume = {90}, pages = {207--216}, doi = {10.1088/0370-1328/90/1/323}, } @Article{LloSmi72, author = {Lloyd, P. and Smith, P. V.}, journal = {Adv. Phys.}, title = {Multiple scattering theory in condensed materials}, year = {1972}, pages = {69--142}, volume = {21}, doi = {10.1080/00018737200101268}, } @Inproceedings{Gaspard91, author = {P. Gaspard}, title = {Scattering resonances: classical and quantum dynamics}, booktitle = {{Quantum Chaos}}, year = {1993}, editor = {G. Casati and I. Guarneri and U. Smilansky}, volume = {19}, isbn = {9781483290324}, series = {Proc. Int. School of Physics Enrico Fermi}, publisher = {North Holland}, } @Article{NorPer68, author = {A. Norcliffe and I. C. Percival}, title = {Correspondence identities: {I}}, journal = {J. Phys. B}, year = {1968}, volume = {1}, pages = {774}, doi = {10.1088/0022-3700/1/5/303}, } @Article{Schulman68, author = {Schulman, L.}, title = {A path integral for spin}, journal = {Phys. Rev.}, year = {1968}, volume = {176}, pages = {1558--1569}, doi = {10.1103/PhysRev.176.1558}, } @Article{Smith60, author = {Smith, F. T.}, title = {Lifetime matrix in collision theory}, journal = {Phys. Rev.}, year = {1960}, volume = {118}, pages = {349--356}, doi = {10.1103/PhysRev.118.349}, } @Article{Friedel58, author = {Friedel, J.}, title = {Metallic alloys}, journal = {Nuovo Cim.}, year = {1958}, volume = {7}, pages = {287--311}, doi = {10.1007/BF02751483}, } @Article{Levi-Civita1906, author = {Levi-Civita, T.}, title = {Sur la r{\'e}solution qualitative du probl{\`e}me restreint des trois corps}, journal = {Acta Math.}, year = {1906}, volume = {30}, pages = {305--327}, doi = {10.1007/BF02418577}, } @Article{Berry_KKR, author = {M. V. Berry}, title = {Quantizing a classically ergodic system: {Sinai's} billiard and the {KKR} method}, journal = {Ann. Phys.}, year = {1981}, volume = {131}, pages = {163--216}, doi = {10.1016/0003-4916(81)90189-5}, } @Article{BalBlo72, author = {R. Balian and C. Bloch}, title = {Distribution of eigenfrequencies for the wave equation in a finite domain: {III. Eigenfrequency} density oscillations}, journal = {Ann. Phys.}, year = {1972}, volume = {69}, pages = {76--160}, doi = {10.1016/0003-4916(72)90006-1}, } @Article{BalBlo74, author = {R. Balian and C. Bloch}, title = {Solution of the {Schr{\"o}dinger} equation in terms of classical paths}, journal = {Ann. Phys.}, year = {1974}, volume = {85}, pages = {514--545}, doi = {10.1016/0003-4916(74)90421-7}, } @Article{aw_chaos, author = {A. Wirzba}, title = {Validity of the semiclassical periodic orbit approximation in the two- and three-disk problems}, journal = {Chaos}, year = {1992}, volume = {2}, pages = {77--83}, doi = {10.1063/1.165901}, } @Article{aw_nucl, author = {A. Wirzba}, title = {Test of the periodic-orbit approximation in n-disk systems}, journal = {Nucl. Phys. A}, year = {1993}, volume = {560}, pages = {136--150}, doi = {10.1016/0375-9474(93)90088-F}, } @InProceedings{vwr_japan, author = {Vattay, G. and Wirzba, A. and Rosenqvist, P. E.}, booktitle = {{Dynamical Systems and Chaos}}, title = {Inclusion of diffraction effects in the {Gutzwiller} trace formula}, year = {1995}, address = {Singapore}, editor = {Y. Aizawa and S. Saito and K. Shiraiwa}, pages = {463}, publisher = {World Scientific}, volume = {2}, url = {https://arXiv.org/abs/chao-dyn/9408005}, } @Article{vwr_stat, author = {Rosenqvist, P. E. and Vattay, G. and Wirzba, A.}, title = {Application of the diffraction trace formula to the three-disk scattering system}, journal = {J. Stat. Phys.}, year = {1996}, volume = {83}, pages = {243--257}, doi = {10.1007/BF02183648}, } @Article{Franz54, author = {W. Franz}, journal = {Z. Naturf. A}, title = {{{{\"U}}ber die Greenschen Funktionen des Zylinders und der Kugel}}, year = {1954}, pages = {705}, volume = {9}, doi = {10.1515/zna-1954-0901}, } @Book{Franz57, title = {{Theorie der Beugung Elektromagnetischer Wellen}}, publisher = {Springer}, year = {1957}, author = {Franz, W.}, address = {Berlin}, isbn = {9783642884658}, doi = {10.1007/978-3-642-88465-8}, } @Article{FraGal55, author = {W. Franz and R. Galle}, journal = {Z. Naturf. A}, title = {{Semiasymptotische Reihen f{\"u}r die Beugung einer ebenen Welle am Zylinder}}, year = {1955}, pages = {374}, volume = {10}, doi = {10.1515/zna-1955-0504}, } @Article{Watson18, author = {G. N. Watson}, title = {The diffraction of electric waves by the earth}, journal = {Proc. R. Soc. Lond. A}, year = {1918}, volume = {95}, pages = {83--99}, url = {http://www.jstor.org/stable/93673}, } @Article{Faulkner77, author = {J. S. Faulkner}, title = {Scattering theory and cluster calculations}, journal = {J. Phys. C}, year = {1977}, volume = {10}, pages = {4661}, doi = {10.1088/0022-3719/10/23/003}, } @Article{Kuipers09, author = {J. Kuipers}, title = {Semiclassics for chaotic systems with tunnel barriers}, journal = {J. Phys. A}, year = {2009}, volume = {42}, pages = {425101}, doi = {10.1088/1751-8113/42/42/425101}, } @Article{EckAur89, author = {B. Eckhardt and E. Aurell}, title = {Convergence of the semi-classical periodic orbit expansion}, journal = {Europhys. Lett.}, year = {1989}, volume = {9}, pages = {509}, doi = {10.1209/0295-5075/9/6/002}, } @Article{WinRic94, author = {D. Wintgen and K. Richter}, title = {Semiclassical nature of planetary atom states}, journal = {Comments At. Mol. Phys.}, year = {1994}, volume = {29}, pages = {261--273}, keywords = {planetary atoms, semiclassical quantization, multipole expansions}, url = {https://epub.uni-regensburg.de/1428/1/ubr04098_ocr.pdf}, } @Article{TanWin95, author = {Tanner, G. and Wintgen, D.}, title = {Semiclassical quantization of intermittency in helium}, journal = {Phys. Rev. Lett.}, year = {1995}, volume = {75}, pages = {2928--2931}, doi = {10.1103/PhysRevLett.75.2928}, } @Article{TaRiRo00, author = {Tanner, G. and Richter, K. and Rost, J.-M.}, title = {The theory of two-electron atoms: between ground state and complete fragmentation}, journal = {Rev. Mod. Phys.}, year = {2000}, volume = {72}, pages = {497--544}, doi = {10.1103/RevModPhys.72.497}, } @Article{KusSti65, author = {P. Kustaanheimo and E. Stiefel}, title = {Perturbation theory of {Kepler} motion based on spinor regularization}, journal = {J. Ang. Math}, year = {1965}, volume = {218}, pages = {204--219}, doi = {10.1515/crll.1965.218.204}, } @Article{Kustaan64, author = {P. Kustaanheimo}, title = {Spinor regularization of the {Kepler} motion}, journal = {Ann. Univ. Turku, Ser. AI.}, year = {1964}, volume = {73}, pages = {204--219}, } @Book{StiSch71, title = {{Linear and Regular Celestial Mechanics}}, publisher = {Springer}, year = {1971}, author = {E. L. Stiefel and G. Scheifele}, address = {New York}, doi = {10.1007/978-3-642-65027-7}, } @Article{RicWin91, author = {K. Richter and D. Wintgen}, title = {Calculations of planetary atom states}, journal = {J. Phys. B}, year = {1991}, volume = {24}, pages = {L565}, doi = {10.1088/0953-4075/24/23/002}, } @Article{Hopf1931, author = {Hopf, H.}, journal = {Math. Ann.}, title = {{{\"U}ber die Abbildungen der dreidimensionalen Sph{\"a}re auf die Kugelfl{\"a}che}}, year = {1931}, pages = {637--665}, volume = {104}, doi = {10.1007/BF01457962}, } @Article{RiTaWi93, author = {Richter, K. and Tanner, G. and Wintgen, D.}, title = {Classical mechanics of two-electron atoms}, journal = {Phys. Rev. A}, year = {1993}, volume = {48}, pages = {4182--4196}, doi = {10.1103/PhysRevA.48.4182}, } @Article{BuWiRo65, author = {A. Burgers and D. Wintgen and J.-M. Rost}, title = {Highly doubly excited {S} states of the helium atom}, journal = {J. Phys. B}, year = {1995}, volume = {28}, pages = {3163}, doi = {10.1088/0953-4075/28/15/010}, } @Article{SiPaSc97, author = {Sieber, M. and Pavloff, N. and Schmit, C.}, title = {Uniform approximation for diffractive contributions to the trace formula in billiard systems}, journal = {Phys. Rev. E}, year = {1997}, volume = {55}, pages = {2279--2299}, doi = {10.1103/PhysRevE.55.2279}, } @Article{PSSU97, author = {H. Primack and H. Schanz and U. Smilansky and I. Ussishkin}, title = {Penumbra diffraction in the semiclassical quantization of concave billiards}, journal = {J. Phys. A}, year = {1997}, volume = {30}, pages = {6693}, doi = {10.1088/0305-4470/30/19/012}, } @Article{Seba90, author = {S\v{e}ba, P.}, title = {Wave chaos in singular quantum billiard}, journal = {Phys. Rev. Lett.}, year = {1990}, volume = {64}, pages = {1855--1858}, doi = {10.1103/PhysRevLett.64.1855}, } @Article{BBLMM95, author = {M. Brack and R. K. Bhaduri and J. Law and Ch. Maier and M. V. N. Murthy}, title = {Effect of a magnetic flux line on the quantum beats in the {H{\'e}non-Heiles} level density}, journal = {Chaos}, year = {1995}, volume = {5}, pages = {317--329}, doi = {10.1063/1.166080}, } @Article{RBMBM96, author = {Reimann, S. M. and Brack, M. and Magner, A. G. and Blaschke, J. and Murthy, M. V. N.}, title = {Circular quantum billiard with a singular magnetic flux line}, journal = {Phys. Rev. A}, year = {1996}, volume = {53}, pages = {39--48}, doi = {10.1103/PhysRevA.53.39}, } @Article{PSSU96, author = {Primack, H. and Schanz, H. and Smilansky, U. and Ussishkin, I.}, title = {Penumbra diffraction in the quantization of dispersing billiards}, journal = {Phys. Rev. Lett.}, year = {1996}, volume = {76}, pages = {1615--1618}, doi = {10.1103/PhysRevLett.76.1615}, } @Article{Keller57, author = {J. B. Keller}, title = {Diffraction by an aperture}, journal = {J. Appl. Phys.}, year = {1957}, volume = {28}, pages = {426--444}, doi = {10.1063/1.1722767}, } @Article{Whelan96, author = {Whelan, N. D.}, title = {Semiclassical quantization using diffractive orbits}, journal = {Phys. Rev. Lett.}, year = {1996}, volume = {76}, pages = {2605--2608}, doi = {10.1103/PhysRevLett.76.2605}, } @Article{Whelan95, author = {Whelan, N. D.}, title = {Geometric and diffractive orbits in the scattering from confocal hyperbolas}, journal = {Phys. Rev. E}, year = {1995}, volume = {51}, pages = {3778--3781}, doi = {10.1103/PhysRevE.51.3778}, } @Article{PavSch91, author = {Pavloff, N. and Schmit, C.}, title = {Diffractive orbits in quantum billiards}, journal = {Phys. Rev. Lett.}, year = {1995}, volume = {75}, pages = {61--64}, doi = {10.1103/PhysRevLett.75.61}, } @Article{DTHvdVVH94, author = {D. Delande and K. T. Taylor and M. H. Halley and van der Veldt, T. and W. Vassen and W. Hogervorst}, title = {Scaled energy spectra of non-hydrogenic {Rydberg} atoms in a magnetic field}, journal = {J. Phys. B}, year = {1994}, volume = {27}, pages = {2771}, doi = {10.1088/0953-4075/27/13/008}, } @Article{RHMW94, author = {G. Raithel and H. Held and L. Marmet and H. Walther}, title = {Rubidium {Rydberg} atoms in strong static fields}, journal = {J. Phys. B}, year = {1994}, volume = {27}, pages = {2849}, doi = {10.1088/0953-4075/27/13/014}, } @Article{CJSK94, author = {Courtney, M. and Jiao, H. and Spellmeyer, N. and Kleppner, D.}, title = {Long-period orbits in the {Stark} spectrum of lithium}, journal = {Phys. Rev. Lett.}, year = {1994}, volume = {73}, pages = {1340--1343}, doi = {10.1103/PhysRevLett.73.1340}, } @Article{ExSeSt89, author = {Exner, P. and {\v{S}}eba, P. and {\v{S}}t'ovi{\v{c}}ek, P.}, title = {On existence of a bound state in an {L}-shaped waveguide}, journal = {Czech. J. Phys. B}, year = {1989}, volume = {39}, pages = {1181--1191}, doi = {10.1007/BF01605319}, } @Article{WuSpMa92, author = {H. Wu and D. W. L. Sprung and J. Martorell}, title = {Electronic properties of a quantum wire with arbitrary bending angle}, journal = {J. Appl. Phys.}, year = {1992}, volume = {72}, pages = {151-154}, doi = {10.1063/1.352176}, } @Article{DMDT95, author = {Dando, P. A. and Monteiro, T. S. and Delande, D. and Taylor, K. T.}, title = {Beyond periodic orbits: {An} example in nonhydrogenic atoms}, journal = {Phys. Rev. Lett.}, year = {1995}, volume = {74}, pages = {1099--1102}, doi = {10.1103/PhysRevLett.74.1099}, } @Article{DaMoOw98, author = {Dando, P. A. and Monteiro, T. S. and Owen, S. M.}, title = {Periodic orbit theory for {Rydberg} atoms in external fields}, journal = {Phys. Rev. Lett.}, year = {1998}, volume = {80}, pages = {2797--2800}, doi = {10.1103/PhysRevLett.80.2797}, } @Article{Carslaw20, author = {Carslaw, H. S.}, title = {Diffraction of waves by a wedge of any angle}, journal = {Proc. London Math. Soc. (Ser. 2)}, year = {1920}, volume = {18}, pages = {291--306}, doi = {10.1112/plms/s2-18.1.291}, } @Article{Sommerfeld1896, author = {Sommerfeld, A.}, title = {{Mathematische Theorie der Diffraction}}, journal = {Mathem. Ann.}, year = {1896}, volume = {47}, pages = {317--374}, doi = {10.1007/BF01447273}, } @Book{Sommerfeld1896en, title = {{Mathematical Theory of Diffraction}}, publisher = {Birkh{\"a}user}, year = {2004}, author = {Sommerfeld, A.}, address = {Boston, MA}, isbn = {978-0-8176-8196-8}, doi = {10.1007/978-0-8176-8196-8_2}, } @Book{Sommerfeld54IV, title = {Optics}, publisher = {Academic Press}, year = {1954}, author = {A. Sommerfeld}, volume = {4}, series = {Lectures on Theoretical Physics}, isbn = {9780126546767}, } @Incollection{BluRei92, author = {R. Bl{\"u}mel and W. P. Reinhardt}, title = {Where is the chaos in two-electron atoms?}, booktitle = {{Directions in Chaos}}, publisher = {World Scientific}, year = {1992}, editor = {D. H. Feng and J.-M. Yuan}, volume = {4}, pages = {245-319}, address = {Singapore}, url = {http://rblumel.faculty.wesleyan.edu/files/2011/06/p49.pdf}, } @Book{Schwicht15, title = {{Physics from Symmetry}}, publisher = {Springer}, year = {2015}, author = {J. Schwichtenberg}, address = {Berlin}, doi = {10.1007/978-3-319-19201-7}, } @Article{Ber-Up, author = {M. V. Berry and C. Upstill}, title = {Catastrophe optics: {Morphologies} of caustics and their diffraction patterns}, journal = {Progr. Optics}, year = {1980}, volume = {18}, pages = {257--346}, doi = {10.1016/s0079-6638(08)70215-4}, } @Article{BoringGuy2, author = {H. Schomerus and M. Sieber}, title = {Bifurcations of periodic orbits and uniform approximations}, journal = {J. Phys. A}, year = {1997}, volume = {30}, pages = {4537}, doi = {10.1088/0305-4470/30/13/010}, } @Article{Thompson16, author = {J. M. T. Thompson}, title = {Chaos, fractals and their applications}, journal = {Int. J. Bifur. Chaos}, year = {2016}, volume = {26}, pages = {1630035}, doi = {10.1142/s0218127416300354}, } @Book{Baladi17, title = {{Dynamical Zeta Functions and Dynamical Determinants for Hyperbolic Maps, A Functional Approach}}, publisher = {Springer}, year = {2017}, author = {Baladi, V.}, address = {Berlin}, url = {https://webusers.imj-prg.fr/~viviane.baladi/baladi-zeta2016.pdf}, } @Book{Huang87, author = {Huang, K.}, publisher = {Wiley}, title = {{Statistical Mechanics}}, year = {1987}, address = {New York}, edition = {2}, isbn = {9780471815181}, } @Book{GohKre69, title = {{Introduction to the Theory of Linear Nonselfadjoint Operators}}, publisher = {Amer. Math. Soc.}, year = {1969}, author = {I. C. Gohberg and M. G. Krein}, volume = {18}, isbn = {978-0-8218-1568-7}, series = {Translations of Mathematical Monographs}, address = {Providence RI}, } @Article{HilTam31, author = {Hille, E. and Tamarkin, J. D.}, title = {On the characteristic values of linear integral equations}, journal = {Acta Math.}, year = {1931}, volume = {57}, pages = {1--76}, doi = {10.1007/BF02403043}, } @Article{Simon77, author = {B. Simon}, journal = {Adv. Math.}, title = {Notes on infinite determinants of {Hilbert} space operators}, year = {1977}, pages = {244--273}, volume = {24}, doi = {10.1016/0001-8708(77)90057-3}, } @Book{Simon71, title = {{Quantum Mechanics for Hamiltonians Defined as Quadratic Forms}}, publisher = {Princeton Univ. Press}, year = {1971}, author = {Simon, B.}, isbn = {9781400868834}, doi = {10.1515/9781400868834}, } @Book{ReeSim76, title = {{Methods of Modern Mathematical Physics: Analysis of Operators}}, publisher = {Academic}, year = {1976}, author = {Reed, M. and Simon, B.}, volume = {4}, isbn = {9780125850049}, note = {Chap. {XIII.17}}, } @Article{vonKoch1901, author = {von Koch, H.}, title = {Sur quelques points de la th{\'e}orie des d{\'e}terminants infinis}, journal = {Acta Math.}, year = {1901}, volume = {24}, pages = {89--122}, doi = {10.1007/BF02403069}, } @Article{Wigner39, author = {E. Wigner}, journal = {Ann. Math.}, title = {On unitary representations of the inhomogeneous {Lorentz} group}, year = {1939}, pages = {149--204}, volume = {40}, url = {http://www.jstor.org/stable/1968551}, } @Article{AlcZei16-1, author = {Alcock-Zeilinger, J. and Weigert, H.}, title = {Simplification rules for birdtrack operators}, journal = {J. Math. Phys.}, year = {2017}, volume = {58}, pages = {051701}, doi = {10.1063/1.4983477}, } @Article{AlcZei16-2, author = {Alcock-Zeilinger, J. and Weigert, H.}, title = {Compact {Hermitian Young} projection operators}, journal = {J. Math. Phys.}, year = {2017}, volume = {58}, pages = {051702}, doi = {10.1063/1.4983478}, } @Article{AlcZei16-3, author = {Alcock-Zeilinger, J. and Weigert, H.}, title = {Transition operators}, journal = {J. Math. Phys.}, year = {2016}, volume = {58}, pages = {051702}, doi = {10.1063/1.4983478}, } @Article{AlcZei16-4, author = {J. Alcock-Zeilinger and H. Weigert}, title = {A simple counting argument of the irreducible representations of {SU(N)} on mixed product spaces}, journal = {J. Algebr. Comb.}, year = {2018}, doi = {10.1007/s10801-018-0853-z}, } @Article{KeppSjo14, author = {Keppeler, S. and Sj{\"o}dahl, M.}, title = {{Hermitian Young} operators}, journal = {J. Math. Phys.}, year = {2014}, volume = {55}, pages = {021702}, doi = {10.1063/1.4865177}, } @Article{CK82, author = {Cvitanovi{\'c}, P. and Kennedy, A. D.}, title = {Spinors in negative dimensions}, journal = {Phys. Scr.}, year = {1982}, volume = {26}, pages = {5--14}, doi = {10.1088/0031-8949/26/1/001}, } @Article{YoungUn, author = {Elvang, H. and Cvitanovi{\'c}, P. and Kennedy, A.D.}, journal = {J. Math. Phys.}, title = {Diagrammatic {Young} projection operators for {U(n)}}, year = {2005}, pages = {043501}, volume = {46}, doi = {10.1063/1.1832753}, } @Article{Young1933, author = {Young, A.}, title = {The application of substitutional analysis to invariants - {III}}, journal = {Phil. Trans. Roy. Soc. Lond. A}, year = {1935}, volume = {234}, pages = {79--114}, doi = {10.1098/rsta.1935.0001}, } @Book{Tung1985na, title = {{Group Theory in Physics}}, publisher = {World Scientific}, year = {1985}, author = {Tung, W.-K.}, doi = {10.1142/0097}, } @Article{Brauer1937, author = {R. Brauer}, title = {On algebras which are connected with the semisimple continuous groups}, journal = {Ann. Math.}, year = {1937}, volume = {38}, pages = {857}, doi = {10.2307/1968843}, } @Incollection{Penrose71, author = {Penrose, R.}, title = {Angular momentum: {An} approach to combinatorical space-time}, booktitle = {{Quantum Theory and Beyond}}, publisher = {Cambridge Univ. Press}, year = {1971}, editor = {Bastin, T.}, address = {Cambridge}, } @Article{tHooft1974jz, author = {{'t Hooft}, G.}, title = {A planar diagram theory for strong interactions}, journal = {Nucl. Phys. B}, year = {1974}, volume = {72}, pages = {461--473}, doi = {10.1016/0550-3213(74)90154-0}, } @Article{Canning1978ee, author = {G. P. Canning}, title = {Diagrammatic group theory in quark models}, journal = {Phys. Rev. D}, year = {1978}, volume = {18}, pages = {395--410}, doi = {10.1103/PhysRevD.18.395}, } @Misc{Mandula81, author = {Mandula, J. E.}, title = {Diagrammatic techniques in group theory}, howpublished = {Univ. of Southampton}, year = {1981}, note = {Notes taken by S. N. Coulson and A. J. G. Hey}, reportnumber = {SHEP 80/81-7}, } @Book{StedmanBook, title = {{Diagram Techniques in Group Theory}}, publisher = {Cambridge U. Press}, year = {1990}, author = {Stedman, G. E.}, address = {Cambridge}, } @Article{Penrose72, author = {Penrose, R. and MacCallum, M. A. H.}, title = {Twistor theory: {An} approach to the quantisation of fields and space-time}, journal = {Phys. Rep.}, year = {1973}, volume = {6}, pages = {241--315}, doi = {10.1016/0370-1573(73)90008-2}, } @Article{Chayut01, author = {Chayut, M.}, title = {From the periphery: the genesis of {Eugene P. Wigner}'s application of group theory to quantum mechanics}, journal = {Found. Chem.}, year = {2001}, volume = {3}, pages = {55--78}, doi = {10.1023/A:1011431408763}, } @Article{Scholz06, author = {E. Scholz}, title = {Introducing groups into quantum theory (1926-1930)}, journal = {Hist. Math.}, year = {2006}, volume = {33}, pages = {440--490}, doi = {10.1016/j.hm.2005.11.007}, } @Article{Bonolis05, author = {L. Bonolis}, title = {{From the Rise of the Group Concept to the Stormy Onset of Group Theory in the New Quantum Mechanics. A} saga of the invariant characterization of physical objects, events and theories}, journal = {Rivista Nuovo Cim.}, year = {2005}, volume = {27}, pages = {1--110}, url = {https://www.researchgate.net/publication/234207946}, } @Book{QuiYi09, title = {{Solid State Physics: Principles and Modern Applications}}, publisher = {Springer}, year = {2009}, author = {Quinn, J. J. and Yi, K .S.}, address = {Berlin}, isbn = {9783540922315}, doi = {10.1007/978-3-540-92231-5}, } @Misc{Wilczak09, author = {R. Wilczak}, title = {Reducing the state-space of the complex {Lorenz} flow}, year = {2009}, note = {{NSF REU} summer 2009 project, {U. of Chicago}}, url = {http://ChaosBook.org/projects/Wilczak/blog.pdf}, } @Article{GuHaSh16, author = {Gur-Ari, G. and Hanada, M. and Shenker, S. H.}, title = {Chaos in classical {D0}-brane mechanics}, journal = {J. High Energy Phys.}, year = {2016}, volume = {2016}, pages = {91}, doi = {10.1007/JHEP02(2016)091}, } @Article{GuQiSt17, author = {Y. Gu and X.-L. Qi and D. Stanford}, title = {Local criticality, diffusion and chaos in generalized {Sachdev-Ye-Kitaev} models}, journal = {J. High Energy Phys.}, year = {2017}, volume = {2017}, pages = {5}, doi = {10.1007/jhep05(2017)125}, } @Article{LarOvc69, author = {Larkin, A. I. and Ovchinnikov, Yu. N.}, title = {Quasiclassical method in the theory of superconductivity}, journal = {Sov. Phys. JETP}, year = {1969}, volume = {28}, pages = {1200--1205}, url = {http://www.jetp.ac.ru/cgi-bin/dn/e_028_06_1200.pdf}, } @Article{LebMou99, author = {P. Leboeuf and A. Mouchet}, title = {Normal forms and complex periodic orbits in semiclassical expansions of {Hamiltonian} systems}, journal = {Ann. Phys.}, year = {1999}, volume = {275}, pages = {54--112}, doi = {10.1006/aphy.1999.5916}, } @Phdthesis{Schmi99, author = {A. Schmiegel}, title = {{Transition to Turbulence in Linearly Stable Shear Flows}}, school = {Philipps-Universit{\"a}t Marburg}, year = {1999}, url = {http://archiv.ub.uni-marburg.de/diss/z2000/0062}, } @Article{Sieber96, author = {M. Sieber}, title = {Uniform approximations for bifurcations of periodic orbits with high repetition numbers}, journal = {J. Phys. A}, year = {1996}, volume = {29}, pages = {4715}, doi = {10.1088/0305-4470/29/15/034}, } @Article{GaoDel97, author = {Gao, J. and Delos, J. B.}, title = {Quantum manifestations of bifurcations of closed orbits in the photoabsorption spectra of atoms in electric fields}, journal = {Phys. Rev. A}, year = {1997}, volume = {56}, pages = {356--364}, doi = {10.1103/PhysRevA.56.356}, } @Article{ShaRob98, author = {Shaw, J. A. and Robicheaux, F.}, title = {Recurrence spectroscopy of atoms in electric fields: {Failure} of classical scaling laws near bifurcations}, journal = {Phys. Rev. A}, year = {1998}, volume = {58}, pages = {1910--1917}, doi = {10.1103/PhysRevA.58.1910}, } @article{MaiWun97, title = {Hydrogen atom in a magnetic field: {Ghost} orbits, catastrophes, and uniform semiclassical approximations}, author = {Main, J. and Wunner, G.}, journal = {Phys. Rev. A}, volume = {55}, pages = {1743--1759}, year = {1997}, doi = {10.1103/PhysRevA.55.1743}, } @Article{BaMaWu00, author = {Bartsch, T. and Main, J. and Wunner, G.}, title = {Ghost orbit bifurcations in semiclassical spectra}, journal = {Progr. Theor. Phys. Suppl.}, year = {2000}, volume = {139}, pages = {429--436}, doi = {10.1143/PTPS.139.429}, } @Book{PosSte78, title = {{Catastrophe Theory and Its Applications}}, publisher = {Dover}, year = {1978}, author = {Poston, T. and Stewart, I.}, address = {New York}, isbn = {9780486692715}, doi = {10.1115/1.3424591}, } @article{DuDelo88, title = {Effect of closed classical orbits on quantum spectra: {Ionization} of atoms in a magnetic field. I. Physical picture and calculations}, author = {Du, M. L. and Delos, J. B.}, journal = {Phys. Rev. A}, volume = {38}, pages = {1896--1912}, numpages = {0}, year = {1988}, doi = {10.1103/PhysRevA.38.1896}, } @Article{Bogomolny89, author = {E. B. Bogomolny}, title = {Photoabsorption by atoms in external fields near the ionization threshold}, journal = {Sov. Phys. JETP}, year = {1989}, volume = {69}, pages = {487--503}, url = {http://www.jetp.ac.ru/cgi-bin/dn/e_069_02_0275.pdf}, } @Article{BrMeTa99, author = {Brack, M. and Meier, P. and Tanaka, K.}, title = {Uniform trace formulae for {SU(2)} and {SO(3)} symmetry breaking}, journal = {J. Phys. A}, year = {1999}, volume = {32}, pages = {331}, doi = {10.1088/0305-4470/32/2/009}, } @book{BabBul91, title={{Short-Wavelength Diffraction Theory: Asymptotic Methods}}, author={Babi{\v{c}}, V. M. and Buldyrev, V. S.}, year={1991}, publisher={Springer}, Address = {New York}, isbn = {978-3-642-83461-5}, } @Article{SarVor94, author = {Saraceno, M. and Voros, A.}, journal = {Physica D}, title = {Towards a semiclassical theory of the quantum baker's map}, year = {1994}, pages = {206 - 268}, volume = {79}, doi = {10.1016/S0167-2789(05)80007-7}, } @Article{BerHow94, author = {M. V. Berry and C. J. Howls}, title = {High orders of the {Weyl} expansion for quantum billiards: resurgence of periodic orbits, and the {Stokes} phenomenon}, journal = {Proc. R. Soc. Lond. A}, year = {1994}, volume = {447}, pages = {527--555}, doi = {10.1098/rspa.1994.0154}, } @Article{BalBlo70, author = {R. Balian and C. Bloch}, title = {Distribution of eigenfrequencies for the wave equation in a finite domain: {I. Three-dimensional} problem with smooth boundary surface}, journal = {Ann. Phys.}, year = {1970}, volume = {60}, pages = {401--447}, doi = {10.1016/0003-4916(70)90497-5}, } @Article{BalBlo71, author = {R. Balian and C. Bloch}, title = {Distribution of eigenfrequencies for the wave equation in a finite domain. {II. Electromagnetic field. Riemannian} spaces}, journal = {Ann. Phys.}, year = {1971}, volume = {64}, pages = {271--307}, doi = {10.1016/0003-4916(71)90286-7}, } @Article{BihKva92, author = {Biham, O. and Kvale, M.}, title = {Unstable periodic orbits in the stadium billiard}, journal = {Phys. Rev. A}, year = {1992}, volume = {46}, pages = {6334--6339}, doi = {10.1103/PhysRevA.46.6334}, } @Article{chicago5, author = {T. C. Halsey and M. H. Jensen and L. P. Kadanoff and I. Procaccia and B. I. Shraiman}, journal = {Phys. Rev. A}, title = {Fractal measures and their singularities: {The} characterization of strange sets}, year = {1986}, pages = {1141--1151}, volume = {33}, doi = {10.1103/PhysRevA.33.1141}, } @Book{ReeSim80, title = {{Methods of Modern Mathematical Physics: Functional analysis}}, publisher = {Academic Press}, year = {1980}, author = {Reed, M. and Simon, B.}, volume = {1}, isbn = {9780125850506}, note = {Chap. {VI}}, } @Article{KeaSie94, author = {J. P. Keating and M. Sieber}, title = {Calculation of spectral determinants}, journal = {Proc. R. Soc. Lond. A}, year = {1994}, volume = {447}, pages = {413--437}, doi = {10.1098/rspa.1994.0148}, } @Book{Birkhoff50vol2, title = {{Collected Mathematical Papers}}, publisher = {Amer. Math. Soc.}, year = {1950}, author = {Birkhoff, G. D.}, volume = {2}, address = {Providence RI}, } @Article{Vernon17, author = {Vernon, J. L.}, title = {Understanding the butterfly effect}, journal = {Amer. Sci.}, year = {2017}, volume = {105}, pages = {130}, url = {https://www.americanscientist.org/article/understanding-the-butterfly-effect}, } @Article{ChNiMo17, author = {Chen, X. and Nishikawa, T. and Motter, A. E.}, title = {Slim fractals: {The} geometry of doubly transient chaos}, journal = {Phys. Rev. X}, year = {2017}, volume = {7}, pages = {021040}, doi = {10.1103/PhysRevX.7.021040}, } @Article{Levin00, author = {Levin, J.}, title = {Gravity waves, chaos, and spinning compact binaries}, journal = {Phys. Rev. Lett.}, year = {2000}, volume = {84}, pages = {3515--3518}, doi = {10.1103/PhysRevLett.84.3515}, } @Article{Cornish00, author = {Cornish, N. J.}, title = {Comment on ``{Gravity} waves, chaos, and spinning compact binaries''}, journal = {Phys. Rev. Lett.}, year = {2000}, volume = {85}, pages = {3980--3980}, doi = {10.1103/PhysRevLett.85.3980}, } @Article{CorFra97, author = {Cornish, N. J. and Frankel, N. E.}, title = {The black hole and the pea}, journal = {Phys. Rev. D}, year = {1997}, volume = {56}, pages = {1903--1907}, doi = {10.1103/PhysRevD.56.1903}, } @Article{KenYor91, author = {Kennedy, J. and Yorke, J. A.}, journal = {Physica D.}, title = {Basins of {Wada}}, year = {1991}, pages = {213 - 225}, volume = {51}, doi = {10.1016/0167-2789(91)90234-Z}, } @Article{DeuPal89, author = {Deutsch, J. M. and Paladin, G.}, title = {Product of random matrices in a microcanonical ensemble}, journal = {Phys. Rev. Lett.}, year = {1989}, volume = {62}, pages = {695--699}, doi = {10.1103/PhysRevLett.62.695}, } @Book{Gray08, title = {{Linear Differential Equations and Group Theory from Riemann to Poincar\'e}}, publisher = {Birkh{\"a}user}, year = {2008}, author = {Gray, J.}, isbn = {9780817647728}, address = {Boston}, } @Article{ElLaTo10, author = {J. R. Elton and A. Lakshminarayan and S. Tomsovic}, title = {Fluctuations in classical sum rules}, journal = {Phys. Rev. E}, year = {2010}, volume = {82}, doi = {10.1103/PhysRevE.82.046223}, } @Article{LiTom17b, author = {Li, J. and Tomsovic, S.}, title = {Exact relations between homoclinic and periodic orbit actions in chaotic systems}, journal = {Phys. Rev. E}, year = {2017}, volume = {97}, pages = {022216}, doi = {10.1103/physreve.97.022216}, } @InCollection{irrational, author = {R. Artuso and P. Cvitanovi{\'c}}, title = {Irrationally winding}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2020}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/paper.shtml#irrational}, } @Article{Bai06, author = {Z.-Q. Bai}, title = {Multifractal analysis of the spectral measure of the {Thue-Morse} sequence: a periodic orbit approach}, journal = {J. Phys. A}, year = {2006}, volume = {39}, pages = {10959}, doi = {10.1088/0305-4470/39/35/002}, } @Article{Bai11, author = {Z.-Q. Bai}, title = {A transfer operator approach to random {Fibonacci} sequences}, journal = {J. Phys. A}, year = {2011}, volume = {44}, pages = {115002}, doi = {10.1088/1751-8113/44/11/115002}, } @Article{Easton91, author = {R. W. Easton}, title = {Transport through chaos}, journal = {Nonlinearity}, year = {1991}, volume = {4}, pages = {583}, doi = {10.1088/0951-7715/4/2/017}, } @Article{GotIse92n, author = {Gotay, M. J. and Isenberg, G. A.}, title = {The symplectization of science}, journal = {Gazette des Math{\'e}maticiens}, year = {1992}, volume = {54}, pages = {59--79}, url = {http://www.pims.math.ca/~gotay/Symplectization(E).pdf}, } @Book{Maxwell1879, author = {Maxwell, J. C.}, editor = {Harman, P. M.}, publisher = {Cambridge Univ. Press}, title = {{The Scientific Letters and Papers of James Clerk Maxwell}}, year = {1995}, address = {Cambridge UK}, isbn = {9780521256261}, note = {V. 1862-1873}, volume = {2}, } @InCollection{CBMarkov, author = {P. Cvitanovi{\'c}}, title = {Walkabout: {Transition} graphs}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2020}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/paper.shtml#Marko}, } @Article{Birkhoff22, author = {Birkhoff, G. D.}, title = {Surface transformations and their dynamical applications}, journal = {Acta Math.}, year = {1922}, volume = {43}, pages = {1--119}, doi = {10.1007/BF02401754}, } @Article{Moser56, author = {Moser, J.}, title = {The analytic invariants of an area-preserving mapping near a hyperbolic fixed point}, journal = {Commun. Pure Appl. Math.}, year = {1956}, volume = {9}, pages = {673--692}, doi = {10.1002/cpa.3160090404}, } @Incollection{LeGhAl13ch5, author = {J. Leys and {\'{E}}. Ghys and A. Alvarez}, title = {Chapter {V : Billiards} - {Duhem's bull}}, booktitle = {{Chaos -- A Mathematical Adventure}}, publisher = {{\'{E}}cole normale sup{\'e}rieure de {Lyon}}, year = {2013}, address = {Lyon}, url = {http://www.chaos-math.org/en/chaos-v-billiards}, } @Article{RanPor13, author = {S. Rankovi{\'c} and M. A. Porter}, title = {Two-particle circular billiards versus randomly perturbed one-particle circular billiards}, journal = {Chaos}, year = {2013}, volume = {23}, pages = {013123}, doi = {10.1063/1.4775756}, } @Article{LaPoBu06, author = {S. Lansel and M. A. Porter and L. A. Bunimovich}, title = {One-particle and few-particle billiards}, journal = {Chaos}, year = {2006}, volume = {16}, pages = {013129}, doi = {10.1063/1.2147740}, } @Article{SawTan13, author = {Sawada, S.-i. and Taniguchi, T.}, title = {Chaos and ergodicity of two hard disks within a circular billiard}, journal = {Phys. Rev. E}, year = {2013}, volume = {88}, pages = {022907}, doi = {10.1103/PhysRevE.88.022907}, } @Article{Malkus72, author = {Malkus, W. V. R.}, title = {Non-periodic convection at high and low {Prandtl} number}, journal = {Mem. Societe Royale des Sciences de Liege}, year = {1972}, pages = {125--128}, } @Misc{AntVas17, author = {J. Antonio-V{\'a}squez}, title = {On the {Pollicott-Ruelle} resonances}, year = {2017}, eprint = {1703.01522}, eprinttype = {arxiv}, } @Misc{Lablee17, author = {Labl{\'e}e, O.}, title = {Trace formulas and zeta functions in spectral seometry}, year = {2017}, url = {https://hal.archives-ouvertes.fr/hal-01504945}, } @TechReport{Rota97, author = {Gian-Carlo Rota}, institution = {Massachusetts Inst. of Technology}, title = {Ten lessons {I} wish {I} had learned before {I} started teaching differential equations}, year = {1997}, note = {Simmons College Meeting of Math. Assoc. of America}, url = {https://web.williams.edu/Mathematics/lg5/Rota.pdf}, } @Misc{Lopez2015, author = {V. L{\'o}pez}, title = {Numerical continuation of invariant solutions of the complex {Ginzburg--Landau} equation}, year = {2015}, eprint = {1502.03862}, eprinttype = {arxiv}, } @Article{MoGrKaTe13, author = {A. E. Motter and M. Gruiz and G. K{\'{a}}rolyi and T. T{\'{e}}l}, title = {Doubly transient chaos: generic form of chaos in autonomous dissipative systems}, journal = {Phys. Rev. Lett.}, year = {2013}, volume = {111}, pages = {065202}, doi = {10.1103/PhysRevLett.111.194101}, } @Article{LaFinOt91, author = {Y.-T. Lau and J. M. Finn and E. Ott}, title = {Fractal dimension in nonhyperbolic chaotic scattering}, journal = {Phys. Rev. Lett.}, year = {1991}, volume = {66}, pages = {978--981}, doi = {10.1103/PhysRevLett.66.978}, } @Misc{Klages08, author = {R. Klages}, title = {From deterministic chaos to anomalous diffusion}, year = {2008}, eprint = {0804.3068}, eprinttype = {arxiv}, } @Book{Sautoy12, title = {{Finding Moonshine: A Mathematician's Journey Through Symmetry}}, publisher = {Harper Collins}, year = {2012}, author = {du Sautoy, M.}, isbn = {9780007380879}, } @InCollection{CBappendDiff, author = {R. Artuso and P. Cvitanovi{\'c}}, title = {Deterministic diffusion}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2020}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/paper.shtml#appendDiff}, } @Article{KimOst86, author = {S. Kim and S. Ostlund}, title = {Simultaneous rational approximations in the study of dynamical systems}, journal = {Phys. Rev. A}, year = {1986}, volume = {34}, pages = {3426--3434}, doi = {10.1103/physreva.34.3426}, } @Article{KimOst85, author = {S. Kim and S. Ostlund}, title = {Renormalization of mappings of the two-torus}, journal = {Phys. Rev. Lett.}, year = {1985}, volume = {55}, pages = {1165--1168}, doi = {10.1103/physrevlett.55.1165}, } @Article{KiOsYu88, author = {S. Kim and S. Ostlund and G. Yu}, title = {Fourier analysis of multi-frequency dynamical systems}, journal = {Physica D}, year = {1988}, volume = {31}, pages = {117--126}, doi = {10.1016/0167-2789(88)90017-6}, } @Article{BGKM91, author = {C. Baesens and J. Guckenheimer and S. Kim and R. S. MacKay}, title = {Three coupled oscillators: mode-locking, global bifurcations and toroidal chaos}, journal = {Physica D}, year = {1991}, volume = {49}, pages = {387--475}, doi = {10.1016/0167-2789(91)90155-3}, } @Article{CheWan91, author = {S.-g. Chen and Y.-q. Wang}, title = {Cubic irrational number and critical scaling law for quasiperiodic motion}, journal = {Phys. Lett. A}, year = {1991}, volume = {153}, pages = {113--116}, doi = {10.1016/0375-9601(91)90850-8}, } @Article{Baldwin92, author = {P. R. Baldwin}, title = {A multidimensional continued fraction and some of its statistical properties}, journal = {J. Stat. Phys.}, year = {1992}, volume = {66}, pages = {1463--1505}, doi = {10.1007/bf01054430}, } @Article{JiHuYi01, author = {Z. Ji-Lin and B. Hu and S. Yi-Sui}, title = {Universal behaviour on the break-up of the spiral mean torus}, journal = {Chin. Phys. Lett.}, year = {2001}, volume = {18}, pages = {1550--1553}, doi = {10.1088/0256-307x/18/12/303}, } @Misc{AnKlKo08, author = {D. V. Anosov and A. V. Klimenko and G. Kolutsky}, title = {On the hyperbolic automorphisms of the 2-torus and their {Markov} partitions}, year = {2008}, url = {https://arXiv.org/abs/0810.5269}, } @InCollection{CBook:PDEs, author = {P. Cvitanovi{\'c}}, title = {Turbulence?}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2020}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/paper.shtml#PDEs}, } @PhdThesis{GilGall18, author = {Gil-Gallegos, S. S.}, title = {{Deterministic Diffusion in Smooth Periodic Potentials}}, school = {Queen Mary Univ.}, year = {2018}, address = {London}, url = {https://qmro.qmul.ac.uk/xmlui/handle/123456789/39750}, } @Article{Johnston18, author = {H. Johnston}, title = {Exotic `non-classical paths' affect quantum interference, experiment confirms}, journal = {Phys. World}, year = {2018}, url = {https://physicsworld.com/a/exotic-non-classical-paths-affect-quantum-interference-experiment-confirms/}, } @Article{RPNSSS18, author = {G. Rengaraj and U. Prathwiraj and S. Narayan Sahoo and R. Somashekhar and U. Sinha}, title = {Measuring the deviation from the superposition principle in interference experiments}, journal = {New J. Phys.}, year = {2018}, volume = {20}, pages = {063049}, doi = {10.1088/1367-2630/aac92c}, } @Article{SCW06, author = {S{\o}ndergaard, N. and Cvitanovi{\'c}, P. and Wirzba, A.}, title = {Periodic orbits in scattering from elastic voids}, journal = {AIP Conference Proceedings}, year = {2006}, volume = {834}, pages = {175--183}, doi = {10.1063/1.2205801}, } @Article{wirzba2005wave, author = {Wirzba, A. and S{\o}ndergaard, N. and Cvitanovi{\'c}, P.}, title = {Wave chaos in elastodynamic cavity scattering}, journal = {Europhys. Lett.}, year = {2005}, volume = {72}, pages = {534--540}, doi = {10.1209/epl/i2005-10286-8}, } @TechReport{Elton08, author = {Elton, J. R.}, title = {An exploration of moderate {Reynolds} number plane {Couette} turbulence}, institution = {School of Physics, Georgia Inst. of Technology}, year = {2007}, url = {http://chaosbook.org/projects/index.shtml\#Elton}, } @Article{Arnold66, author = {V. I. Arnol'd}, title = {Sur la g{\'{e}}om{\'{e}}trie diff{\'{e}}rentielle des groupes de {Lie} de dimension infinie et ses applications {\`{a}} l'hydrodynamique des fluides parfaits}, journal = {Ann. Inst. Fourier}, year = {1966}, volume = {16}, pages = {319--361}, doi = {10.5802/aif.233}, } @Article{Dong18, author = {C. Dong}, title = {Organization of the periodic orbits in the {R{\"o}ssler} flow}, journal = {Int. J. Mod. Phys. B}, year = {2018}, volume = {22}, pages = {1850227}, doi = {10.1142/s0217979218502272}, } @Article{BaBlSe09, author = {R. Barrio and F. Blesa and S. Serrano}, title = {Qualitative analysis of the {R{\"o}ssler} equations: {Bifurcations} of limit cycles and chaotic attractors}, journal = {Physica D}, year = {2009}, volume = {238}, pages = {1087--1100}, doi = {10.1016/j.physd.2009.03.010}, } @Article{CheChe17, author = {A.-L. Cheng and Y.-Y. Chen}, title = {Analytical study of funnel type {R{\"o}ssler} attractor}, journal = {Chao}, year = {2017}, volume = {27}, pages = {073117}, doi = {10.1063/1.4995962}, } @Article{GupYad17, author = {M. K. Gupta and C. K. Yadav}, title = {Jacobi stability analysis of {R{\"o}ssler} system}, journal = {Int. J. Bifur. Chaos}, year = {2017}, volume = {27}, pages = {1750056}, doi = {10.1142/s0218127417500560}, } @PhdThesis{Raju18, author = {A. Raju}, title = {Aspects of the renormalization group}, school = {Physics Dept., Cornell Univ.}, year = {2018}, url = {http://www.lassp.cornell.edu/sethna/pubPDF/RajuPhD.pdf}, } @Article{RCHKLRS17, author = {Raju, A. and Clement, . B. and Hayden, L. X. and Kent-Dobias, J. P. and Liarte, D. B. and Rocklin, D. Z. and Sethna, J. P.}, journal = {Phys. Rev. X}, title = {Normal form for renormalization groups}, year = {2019}, pages = {021014}, volume = {9}, doi = {10.1103/PhysRevX.9.021014}, } @Article{RaMaSe17, author = {Raju, A. and Machta, B. B. and Sethna, J. P.}, journal = {Phys. Rev. E}, title = {Information loss under coarse graining: {A} geometric approach}, year = {2018}, pages = {052112}, volume = {98}, doi = {10.1103/PhysRevE.98.052112}, } @Misc{RajSet18, author = {A. Raju and J. P. Sethna}, title = {Reexamining the renormalization group: {Period} doubling onset of chaos}, year = {2018}, url = {http://arxiv.org/abs/1807.09517}, } @Book{Zee10, author = {Zee, A.}, publisher = {Princeton Univ. Press}, title = {{Quantum Field Theory in a Nutshell}}, year = {2010}, address = {Princeton NJ}, edition = {2}, isbn = {9781400835324}, } @Article{Dong18a, author = {C. Dong}, title = {Topological classification of periodic orbits in {Lorenz} system}, journal = {Chin. Phys. B}, year = {2018}, volume = {27}, pages = {080501}, doi = {10.1088/1674-1056/27/8/080501}, } @Article{Dong18b, author = {C. Dong}, title = {Topological classification of periodic orbits in the {Yang-Chen} system}, journal = {Europhys. Lett.}, year = {2018}, volume = {123}, pages = {20005}, doi = {10.1209/0295-5075/123/20005}, } @Article{Dong18c, author = {C. Dong}, title = {Topological classification of periodic orbits in the {Kuramoto-Sivashinsky} equation}, journal = {Mod. Phys. Lett. B}, year = {2018}, volume = {32}, pages = {1850155}, doi = {10.1142/s0217984918501555}, } @Article{DWDUL16, author = {C. Dong and P. Wang and M. Du and T. Uzer and Y. Lan}, title = {The ionized electron return phenomenon of {Rydberg} atom in crossed-fields}, journal = {Mod. Phys. Lett. B}, year = {2016}, volume = {30}, pages = {1650183}, doi = {10.1142/s0217984916501839}, } @Book{Coleman15, title = {{Introduction to Many-Body Physics}}, publisher = {Cambridge Univ. Press}, year = {2015}, author = {P. Coleman}, address = {Cambridge UK}, doi = {10.1017/cbo9781139020916}, } @Book{AltlSim09, title = {{Condensed Matter Field Theory}}, publisher = {Cambridge Univ. Press}, year = {2009}, author = {A. Altland and B. D. Simons}, address = {Cambridge UK}, doi = {10.1017/cbo9780511789984}, } @Book{gilmore08, author = {R. Gilmore}, publisher = {Cambridge Univ. Press}, title = {{Lie Groups, Physics, and Geometry}}, year = {2008}, address = {Cambridge UK}, doi = {10.1017/cbo9780511791390}, } @Article{Miles15, author = {R. Miles}, title = {A dynamical zeta function for group actions}, journal = {Monatsh. Math.}, year = {2016}, volume = {182}, pages = {683--708}, doi = {10.1007/s00605-016-0909-x}, } @Article{Ruelle02, author = {D. Ruelle}, title = {Dynamical zeta functions and transfer operators}, journal = {Notices Amer. Math. Soc.}, year = {2002}, volume = {95}, pages = {887--895}, url = {https://www.ams.org/notices/200208/fea-ruelle.pdf}, } @InCollection{Sharp04, author = {R. Sharp}, title = {Periodic orbits of hyperbolic flows}, booktitle = {{On Some Aspects of the Theory of Anosov Systems}}, publisher = {Springer}, year = {2004}, editor = {G. A. Margulis}, pages = {73--138}, address = {Berlin}, doi = {10.1007/978-3-662-09070-1_2}, } @Book{Faddeev95, title = {{40 Years in Mathematical Physics}}, publisher = {World Scientific}, year = {1995}, author = {Faddeev, L. D.}, address = {Singapore}, isbn = {9789810221997}, } @Article{Faddeev88, author = {Faddeev, L. D.}, title = {Thirty years in mathematical physics}, journal = {Proc. Steklov Inst. Math.}, year = {1988}, volume = {176}, pages = {3--28}, url = {http://mi.mathnet.ru/eng/tm2122}, } @Misc{Kardar14, author = {M. Kardar}, title = {{8.334 Statistical Mechanics II: Statistical Physics of Fields}}, howpublished = {MIT OpenCourseWare}, year = {2014}, url = {https://ocw.mit.edu/courses/physics/8-334-statistical-mechanics-ii-statistical-physics-of-fields-spring-2014/}, } @InCollection{Kardar14lec23, author = {M. Kardar}, title = {Two dimensional solids, two dimensional melting}, booktitle = {{8.334 Statistical Mechanics II: Statistical Physics of Fields}}, publisher = {MIT OpenCourseWare}, year = {2014}, address = {Cambridge MA}, url = {https://ocw.mit.edu/courses/physics/8-334-statistical-mechanics-ii-statistical-physics-of-fields-spring-2014/lecture-notes/MIT8_334S14_Lec23.pdf}, } @Article{Weich15, author = {T. Weich}, title = {Resonance chains and geometric limits on {Schottky} surfaces}, journal = {Commun. Math. Phys.}, year = {2015}, volume = {337}, pages = {727--765}, doi = {10.1007/s00220-015-2359-z}, } @Article{PolVyt18, author = {Pollicott, M. and Vytnova, P.}, title = {Zeros of the {Selberg} zeta function for symmetric infinite area hyperbolic surfaces}, journal = {Geometriae Dedicata}, year = {2018}, volume = {197}, pages = {1--32}, doi = {10.1007/s10711-018-0386-6}, } @Article{Mainieri95a, author = {R. Mainieri}, title = {Cycle expansions with pruned orbits have branch points}, journal = {Physica D}, year = {1995}, volume = {83}, pages = {206--215}, doi = {10.1016/0167-2789(94)00263-p}, } @Article{BauMai97, author = {O. Bauer and R. Mainieri}, title = {The convergence of chaotic integrals}, journal = {Chaos}, year = {1997}, volume = {7}, pages = {361--367}, doi = {10.1063/1.166251}, } @Article{WaWaLa18, author = {D. Wang and P. Wang and Y. Lan}, title = {Accelerated variational approach for searching cycles}, journal = {Phys. Rev. E}, year = {2018}, volume = {98}, pages = {042204}, doi = {10.1103/physreve.98.042204}, } @Article{ZhoRenE08, author = {Zhou, X. and Ren, W. and {E}, W.}, journal = {J. Chem. Phys.}, title = {Adaptive minimum action method for the study of rare events}, year = {2008}, pages = {104111}, volume = {128}, doi = {10.1063/1.2830717}, } @Article{BurMit18, author = {K. Burke and K. Mitchell}, title = {A surface of section for hydrogen in crossed electric and magnetic fields}, journal = {Mathematics}, year = {2018}, volume = {6}, pages = {185}, doi = {10.3390/math6100185}, } @TechReport{Sommer15, author = {Sommer, R.}, title = {{Introduction to Lattice Gauge Theories}}, institution = {Humboldt Univ.}, year = {2015}, url = {https://www-zeuthen.desy.de/alpha/lgt25-11-11.pdf}, } @TechReport{Wiese09, author = {U.-J. Wiese}, title = {{An Introduction to Lattice Field Theory}}, institution = {Univ. Bern}, year = {2009}, url = {http://www.wiese.itp.unibe.ch/lectures/lattice.pdf}, } @Book{Rothe05, title = {{Lattice Gauge Theories - An Introduction}}, publisher = {World Scientific}, year = {2005}, author = {H. J. Rothe}, address = {Singapore}, doi = {10.1142/5674}, } @Book{MonMun94, author = {I. Montvay and G. M{\"u}nster}, publisher = {Cambridge Univ. Press}, title = {{Quantum Fields on a Lattice}}, year = {1994}, address = {Cambridge UK}, doi = {10.1017/cbo9780511470783}, } @Book{Smit02, author = {Smit, J.}, publisher = {Cambridge Univ. Press}, title = {{Introduction to Quantum Fields on a Lattice}}, year = {2002}, address = {Cambridge UK}, doi = {10.1017/cbo9780511583971}, } @Misc{MunWal00, author = {G. M{\"u}nster and M. Walzl}, title = {Lattice gauge theory - {A} short primer}, year = {2000}, eprint = {hep-lat/0012005}, eprintclass = {hep-lat}, eprinttype = {arxiv}, } @Article{ZiReMc09, author = {R. K. P. Zia and E. F. Redish and S. R. McKay}, title = {Making sense of the {Legendre} transform}, journal = {Am. J. Phys}, year = {2009}, volume = {77}, pages = {614--622}, doi = {10.1119/1.3119512}, } @Article{KauRie08, author = {B. Krauskopf and T. Rie{\ss}}, title = {A {Lin's} method approach to finding and continuing heteroclinic connections involving periodic orbits}, journal = {Nonlinearity}, year = {2008}, volume = {21}, pages = {1655--1690}, doi = {10.1088/0951-7715/21/8/001}, } @Article{Lin90, author = {X.-B. Lin}, title = {Using {Melnikov's} method to solve {Silnikov's} problems}, journal = {Proc. R. Soc. Edinb. A}, year = {1990}, volume = {116}, pages = {295--325}, doi = {10.1017/s0308210500031528}, } @Article{Petrisor13, author = {E. Petrisor}, title = {Twist number and order properties of periodic orbits}, journal = {Physica D}, year = {2013}, volume = {263}, pages = {57--73}, doi = {10.1016/j.physd.2013.08.001}, } @Incollection{Meyer14, author = {H. B. Meyer}, title = {Lattice {QCD}: {A} brief introduction}, booktitle = {{Lattice {QCD} for Nuclear Physics}}, publisher = {Springer}, year = {2014}, editor = {H.-W. Lin and H. B. Meyer}, pages = {1--34}, address = {York New}, doi = {10.1007/978-3-319-08022-2_1}, } @Article{Jansen07, author = {K. Jansen}, title = {Lattice field theory}, journal = {Int. J. Mod. Phys. E}, year = {2007}, volume = {16}, pages = {2638--2679}, doi = {10.1142/s0218301307008355}, } @Article{MurZen18, author = {Murgan, R. and Zender, A.}, title = {Energy eigenvalues of the three-dimensional quantum harmonic oscillator from {SU}(3) cubic {Casimir} operator}, journal = {Eur. J. Phys.}, year = {2018}, volume = {40}, pages = {015405}, doi = {10.1088/1361-6404/aaee38}, } @Article{BanItz66, author = {Bander, M. and Itzykson, C.}, title = {Group theory and the hydrogen atom {(I)}}, journal = {Rev. Mod. Phys.}, year = {1966}, volume = {38}, pages = {330--345}, doi = {10.1103/revmodphys.38.330}, } @Misc{ROAC18, author = {Radice, M. and Onofri, M. and Artuso, R. and Cristadoro, G.}, title = {Environment-averaged {L{\'e}vy-Lorentz} gas}, year = {2018}, eprint = {1811.10252}, eprinttype = {arxiv}, } @Article{ViPrKr17, author = {A. Villois and D. Proment and G. Krstulovic}, title = {Universal and nonuniversal aspects of vortex reconnections in superfluids}, journal = {Phys. Rev. Fluids}, year = {2017}, volume = {2}, pages = {044701}, doi = {10.1103/physrevfluids.2.044701}, } @Article{IMAD15, author = {I. Ispolatov and V. Madhok and S. Allende and M. Doebeli}, title = {Chaos in high-dimensional dissipative dynamical systems}, journal = {Sci. Rep.}, year = {2015}, volume = {5}, pages = {12506}, doi = {10.1038/srep12506}, } @Article{Haugaard17, author = {A. M. Haugaard}, title = {Predicting the bounds of large chaotic systems using low-dimensional manifolds}, journal = {PLoS One}, year = {2017}, volume = {12}, pages = {e0179507}, doi = {10.1371/journal.pone.0179507}, } @Misc{FiMaFu18, author = {Fiol, B. and Mart{\'i}nez-Montoya, J. and Rios Fukelman, A.}, title = {Wilson loops in terms of color invariants}, year = {2018}, eprint = {1812.06890}, eprinttype = {arxiv}, } @Article{Luque2012, author = {B. Luque and F. J. Ballesteros and A. M. N{\'u}{\~n}ez and A. Robledo}, title = {Quasiperiodic graphs: {Structural} design, scaling and entropic properties}, journal = {J. Nonlin Sci.}, year = {2012}, volume = {23}, pages = {335--342}, doi = {10.1007/s00332-012-9153-2}, } @Article{Datseris18, author = {Datseris, G.}, title = {{DynamicalSystems}.jl: {A Julia} software library for chaos and nonlinear dynamics}, journal = {J. Open Source Soft.}, year = {2018}, volume = {3}, pages = {598}, doi = {10.21105/joss.00598}, } @Article{KatEfr19, author = {Katz-Saporta, O. and Efrati, E.}, title = {Self-driven fractional rotational diffusion of the harmonic three-mass system}, journal = {Phys. Rev. Lett.}, year = {2019}, volume = {122}, pages = {024102}, doi = {10.1103/physrevlett.122.024102}, } @Article{MIAKU18, author = {Y. Miino and D. Ito and H. Asahara and T. Kousaka and T. Ueta}, title = {A general method to stabilize unstable periodic orbits for switched dynamical systems with a periodically moving threshold}, journal = {Int. J. Circuit Theory Appl.}, year = {2018}, volume = {46}, pages = {2380--2393}, doi = {10.1002/cta.2573}, } @Article{HKOS18, author = {S. Hittmeyer and B. Krauskopf and H. M. Osinga and K. Shinohara}, title = {Existence of blenders in a {H{\'e}non}-like family: geometric insights from invariant manifold computations}, journal = {Nonlinearity}, year = {2018}, volume = {31}, pages = {R239--R267}, doi = {10.1088/1361-6544/aacd66}, } @Article{GKSR18, author = {Gil-Gallegos, S. S. and Klages, R. and Solanp{\"a}{\"a}, J. and R{\"a}s{\"a}nen, E.}, title = {Energy-dependent diffusion in a soft periodic {Lorentz} gas}, journal = {Eur. Phys. J. Special Topics}, year = {2019}, volume = {228}, pages = {143--160}, doi = {10.1140/epjst/e2019-800136-8}, } @Article{Datseris17, author = {Datseris, G.}, title = {{DynamicalBilliards}.jl: {An} easy-to-use, modular and extendable {Julia} package for dynamical billiard systems in two dimensions}, journal = {J. Open Source Soft.}, year = {2017}, volume = {2}, pages = {458}, doi = {10.21105/joss.00458}, } @Article{Shepelyansky14, author = {D. Shepelyansky}, title = {Early chaos theory}, journal = {Phys. Today}, year = {2014}, volume = {67}, pages = {10--10}, doi = {10.1063/pt.3.2292}, } @Article{Ruelle14, author = {D. Ruelle}, title = {Early chaos theory}, journal = {Phys. Today}, year = {2014}, volume = {67}, pages = {9--10}, doi = {10.1063/pt.3.2291}, } @Article{MotCam13, author = {A. E. Motter and D. K. Campbell}, title = {Chaos at fifty}, journal = {Phys. Today}, year = {2013}, volume = {66}, pages = {27--33}, doi = {10.1063/pt.3.1977}, } @Book{KotSer71, title = {{Collection of Problems in Classical Mechanics}}, publisher = {Elsevier}, year = {2013}, author = {Kotkin, G. L. and Serbo, V. G.}, isbn = {9781483186610}, } @Article{DHPv08, author = {Diks, C. and Hommes, C. and Panchenko, V. and van der Weide, R.}, title = {{E{\&}F Chaos: A} user friendly software package for nonlinear economic dynamics}, journal = {Computational Econ.}, year = {2008}, volume = {32}, pages = {221--244}, doi = {10.1007/s10614-008-9130-x}, } @Article{IshSan98, author = {Ishii, Y. and Sands, D.}, title = {Monotonicity of the {Lozi} family near the tent-maps}, journal = {Commun. Math. Phys.}, year = {1998}, volume = {198}, pages = {397--406}, doi = {10.1007/s002200050482}, } @Article{Harter78II, author = {Harter, W. G. and dos Santos, N.}, title = {Double-group theory on the half-shell and the two-level system. {II}. {Optical} polarization}, journal = {Am. J. Phys}, year = {1978}, volume = {46}, pages = {264--273}, doi = {10.1119/1.11135}, } @Misc{LaShMe18, author = {Lasagna, D. and Sharma, A. and Meyers, J.}, title = {Periodic shadowing sensitivity analysis of chaotic systems}, year = {2018}, eprint = {1806.02077}, eprinttype = {arxiv}, } @Article{Lasagna17, author = {D. Lasagna}, title = {Sensitivity analysis of systems using unstable periodic orbits}, journal = {SIAM J. Appl. Dyn. Syst.}, year = {2018}, volume = {17}, pages = {547--580}, doi = {10.1137/17M114354X}, } @Article{LY75, author = {Li, T.-Y. and Yorke, J. A.}, title = {Period three implies chaos}, journal = {Amer. Math. Monthly}, year = {1975}, volume = {82}, pages = {985--992}, doi = {10.1080/00029890.1975.11994008}, } @Article{BBCDS92, author = {J. Banks and J. Brooks and G. Cairns and G. Davis and P. Stacey}, title = {{On Devaney's} definition of chaos}, journal = {Amer. Math. Monthly}, year = {1992}, volume = {99}, pages = {332--334}, doi = {10.1080/00029890.1992.11995856}, } @Article{Crannell95, author = {Crannell, A.}, title = {The role of transitivity in {Devaney's} definition of chaos}, journal = {Amer. Math. Monthly}, year = {1995}, volume = {102}, pages = {788--793}, doi = {10.1080/00029890.1995.12004662}, } @Article{Touhey97, author = {P. Touhey}, title = {Yet another definition of chaos}, journal = {Amer. Math. Monthly}, year = {1997}, volume = {104}, pages = {411--414}, doi = {10.1080/00029890.1997.11990658}, } @Article{HunOtt15, author = {Hunt, B. R. and Ott, E.}, title = {Defining chaos}, journal = {Chaos}, year = {2015}, volume = {25}, pages = {097618}, doi = {10.1063/1.4922973}, } @Article{SmyPap91, author = {Y. S. Smyrlis and D. T. Papageorgiou}, title = {Predicting chaos for infinite dimensional dynamical systems: the {Kuramoto-Sivashinsky} equation, a case study}, journal = {Proc. Natl. Acad. Sci. USA}, year = {1991}, volume = {88}, pages = {11129--11132}, doi = {10.1073/pnas.88.24.11129}, } @TechReport{AlcZei18, author = {Alcock-Zeilinger, J. M.}, title = {{The Special Unitary Group, Birdtracks, and Applications in QCD}}, institution = {Univ. T{\"u}bingen}, year = {2018}, url = {https://www.math.uni-tuebingen.de/de/forschung/maphy/lehre/ss-2018/sun/dateien/birdtracks-sun-qcd-lecturenotes.pdf}, } @Article{BiHoNi96, author = {V. N. Biktashev and A. V. Holden and E. V. Nikolaev}, title = {Spiral wave meander and symmetry of the plane}, journal = {Int. J. Bifur. Chaos}, year = {1996}, volume = {6}, pages = {2433--2440}, doi = {10.1142/s0218127496001582}, } @Book{Schutz85, author = {Schutz, B. F.}, publisher = {Cambridge Univ. Press}, title = {{A First Course in General Relativity}}, year = {1985}, address = {Cambridge UK}, doi = {10.1017/cbo9780511984181}, } @Article{KobSak17, author = {Kobayashi, M. U. and Saiki, Y.}, title = {Network analysis of chaotic systems through unstable periodic orbits}, journal = {Chaos}, year = {2017}, volume = {27}, pages = {081103}, doi = {10.1063/1.4995043}, } @Article{Hill86, author = {G. W. Hill}, title = {On the part of the motion of the lunar perigee which is a function of the mean motions of the sun and moon}, journal = {Acta Math.}, year = {1886}, volume = {8}, pages = {1--36}, doi = {10.1007/bf02417081}, } @Misc{GuBuCv17, author = {M. Gudorf and P. Cvitanovi{\'c}}, title = {Spatiotemporal tiling of the {Kuramoto-Sivashinsky} flow}, year = {2019}, note = {In preparation}, } @PhdThesis{GudorfThesis, author = {Gudorf, M. N.}, title = {Spatiotemporal formulation of the {Kuramoto-Sivashinsky} equation}, school = {School of Physics, Georgia Inst. of Technology}, year = {2019}, address = {Atlanta}, url = {http://ChaosBook.org/projects/theses.html}, } @PhdThesis{DingThesis, author = {Ding, X.}, title = {{Geometry of Inertial Manifolds in Nonlinear Dissipative Dynamical Systems}}, school = {School of Physics, Georgia Inst. of Technology}, year = {2017}, address = {Atlanta}, url = {http://ChaosBook.org/projects/theses.html}, } @Article{KGSSR18, author = {Klages, R. and Gil-Gallegos, S. S. and Solanp{\"a}{\"a}, J. and Sarvilahti, M. and R{\"a}s{\"a}nen, E.}, title = {Normal and anomalous diffusion in soft {Lorentz} gases}, journal = {Phys. Rev. Lett.}, year = {2019}, volume = {122}, doi = {10.1103/physrevlett.122.064102}, } @Article{GeDeAl12, author = {Georgiou, O. and Dettmann, C. P. and Altmann, E. G.}, title = {Faster than expected escape for a class of fully chaotic maps}, journal = {Chaos}, year = {2012}, volume = {22}, pages = {043115}, doi = {10.1063/1.4766723}, } @Article{AEOGS10, author = {Avlund, M. and Ellegaard, C. and Oxborrow, M. and Guhr, T. and S\o{}ndergaard, N.}, title = {Observation of periodic orbits on curved two-dimensional geometries}, journal = {Phys. Rev. Lett.}, year = {2010}, volume = {104}, pages = {164101}, doi = {10.1103/PhysRevLett.104.164101}, } @Book{HaCh08, title = {{Nonlinear Dynamical Systems and Control: A {Lyapunov}-Based Approach}}, publisher = {Princeton Univ. Press}, year = {2008}, author = {Haddad, W. M. and Chellaboina, V.}, address = {Princeton NJ}, } @Article{SlBaJu13, author = {J. Slipantschuk and O. F. Bandtlow and W. Just}, title = {On the relation between {Lyapunov} exponents and exponential decay of correlations}, journal = {J. Phys. A}, year = {2013}, volume = {46}, pages = {075101}, doi = {10.1088/1751-8113/46/7/075101}, } @Book{PerRich82N, author = {I. Percival and D. Richards}, publisher = {Cambridge Univ. Press}, title = {{Introduction to Dynamics}}, year = {1996}, address = {Cambridge UK}, isbn = {9780521281492}, } @Book{LuoGuo12, title = {{Vibro-impact Dynamics}}, publisher = {Wiley}, year = {2013}, author = {Luo, A. C. J. and Guo, Y.}, address = {New York}, doi = {10.1002/9781118402924}, } @Book{hao89, title = {{Elementary Symbolic Dynamics and Chaos in Dissipative Systems}}, publisher = {World Scientific}, year = {1989}, author = {Hao, B.-L.}, address = {Singapore}, doi = {10.1142/0674}, } @Misc{FauTsu12, author = {Faure, F. and Tsujii, M.}, title = {Prequantum transfer operator for symplectic {Anosov} diffeomorphism}, year = {2012}, url = {https://hal.archives-ouvertes.fr/hal-00703234/}, } @Article{FauTsu13, author = {Faure, F. and Tsujii, M.}, title = {Band structure of the {Ruelle} spectrum of contact {Anosov} flows}, journal = {C.R. Math.}, year = {2013}, volume = {351}, pages = {385--391}, doi = {10.1016/j.crma.2013.04.022}, } @Article{Faure07, author = {F. Faure}, title = {Prequantum chaos: {Resonances} of the prequantum cat map}, journal = {J. Modern Dynamics}, year = {2007}, volume = {1}, pages = {255--285}, doi = {10.3934/jmd.2007.1.255}, } @Article{FaRoSj08, author = {Faure, F. and Roy, N. and Sj{\"o}strand, J.}, title = {Semi-classical approach for {Anosov} diffeomorphisms and {Ruelle} resonances}, journal = {Open Math. J.}, year = {2008}, volume = {1}, pages = {35--81}, doi = {10.2174/1874117700801010035}, } @Article{Faure11, author = {Faure, F.}, title = {Semiclassical origin of the spectral gap for transfer operators of a partially expanding map}, journal = {Nonlinearity}, year = {2011}, volume = {24}, pages = {1473--1498}, doi = {10.1088/0951-7715/24/5/005}, } @Article{StrMag76, author = {Strutinsky, V. M. and Magner, A. G.}, title = {Quasiclassical theory of nuclear shell structure}, journal = {Sov. J. Particles Nucl.}, year = {1976}, volume = {7}, pages = {138--163}, } @Article{SeoSan12, author = {J. M. Seoane, M. A. F. Sanju\'an}, title = {New developments in classical chaotic scattering}, journal = {Rep. Prog. Phys.}, year = {2013}, volume = {76}, pages = {016001}, doi = {10.1088/0034-4885/76/1/016001}, } @InProceedings{KuKuSa05, author = {Kuznetsov, S. P. and Kuznetsov, A. P. and Sataev, I. R.}, booktitle = {{Physics and Control, 2005 Internat. Conference Proc.}}, title = {Review and examples of non-{Feigenbaum} critical situations associated with period-doubling}, year = {2005}, pages = {610--615}, doi = {10.1109/PHYCON.2005.1514057}, } @Article{Lesne07, author = {A. Lesne}, title = {The discrete versus continuous controversy in physics}, journal = {Math. Struct. Computer Sci.}, year = {2007}, volume = {17}, pages = {185--223}, doi = {10.1017/S0960129507005944}, } @Book{Feldman19, author = {Feldman, D.}, publisher = {Princeton Univ. Press}, title = {{Chaos and Dynamical Systems}}, year = {2019}, isbn = {9780691189390}, doi = {10.1515/9780691189390}, } @Article{LiTom19, author = {Li, J. and Tomsovic, S.}, title = {Exact decomposition of homoclinic orbit actions in chaotic systems: {Information} reduction}, journal = {Phys. Rev. E}, year = {2019}, volume = {99}, pages = {032212}, doi = {10.1103/physreve.99.032212}, } @Article{BeiGal97, author = {Beims, M. W. and Gallas, J. A. C.}, title = {Accumulation points in nonlinear parameter lattices}, journal = {Physica A}, year = {1997}, volume = {238}, pages = {225--244}, doi = {10.1016/s0378-4371(96)00451-7}, } @Article{SanYor13, author = {Sander, E. and Yorke, J. A.}, title = {A period-doubling cascade precedes chaos for planar maps}, journal = {Chaos}, year = {2013}, volume = {23}, pages = {033113}, doi = {10.1063/1.4813600}, } @Article{Daido81, author = {Daido, H.}, title = {Universal relation of a band-splitting sequence to a preceding period-doubling one}, journal = {Phys. Lett. A}, year = {1981}, volume = {86}, pages = {259--262}, doi = {10.1016/0375-9601(81)90360-1}, } @Article{Daido82, author = {H. Daido}, title = {Period-doubling bifurcations and associated universal properties including parameter dependence}, journal = {Progr. Theor. Phys.}, year = {1982}, volume = {67}, pages = {1698--1723}, doi = {10.1143/ptp.67.1698}, } @Article{Lorenz80, author = {E. N. Lorenz}, title = {Noisy periodicity and reverse bifurcation}, journal = {Ann. New York Acad. Sci.}, year = {1980}, volume = {357}, pages = {282--291}, doi = {10.1111/j.1749-6632.1980.tb29693.x}, url = {http://eaps4.mit.edu/research/Lorenz/Noisy_Periodicity_1980.pdf}, } @Article{DeGrPo79, author = {Derrida, B. and Grevois, A. and Pomeau, Y.}, title = {Universal metric properties of bifurcations of endomorphisms}, journal = {J. Phys. A}, year = {1979}, volume = {12}, pages = {269--296}, doi = {10.1088/0305-4470/12/3/004}, } @Article{Grassberger81, author = {P. Grassberger}, title = {On the {Hausdorff} dimension of fractal attractors}, journal = {J. Stat. Phys.}, year = {1981}, volume = {26}, pages = {173--179}, doi = {10.1007/bf01106792}, } @Article{HuMao82, author = {B. Hu and J. M. Mao}, title = {Period doubling: {Universality} and critical-point order}, journal = {Phys. Rev. A}, year = {1982}, volume = {25}, pages = {3259--3261}, doi = {10.1103/physreva.25.3259}, } @Article{Mendes81, author = {Vilela Mendes, R.}, title = {Critical-point dependence of universality in maps of the interval}, journal = {Phys. Lett. A}, year = {1981}, volume = {84}, pages = {1--3}, doi = {10.1016/0375-9601(81)90002-5}, } @Article{KurKog82, author = {Y. Kuramoto and S. Koga}, title = {Anomalous period-doubling bifurcations leading to chemical turbulence}, journal = {Phys. Lett. A}, year = {1982}, volume = {92}, pages = {1--4}, doi = {10.1016/0375-9601(82)90725-3}, } @Article{MauLib80, author = {J. Maurer and A. Libchaber}, title = {Effect of the {Prandtl} number on the onset of turbulence in liquid {4He}}, journal = {J. Physique Lett.}, year = {1980}, volume = {41}, pages = {515--518}, doi = {10.1051/jphyslet:019800041021051500}, } @Article{CoEcKo81, author = {Collet, P. and Eckmann, J.-P. and Koch, H.}, title = {Period doubling bifurcations for families of maps on {$R_n$}}, journal = {J. Stat. Phys.}, year = {1981}, volume = {25}, pages = {1--14}, doi = {10.1201/9780203734636-37}, } @Article{Hu82, author = {Hu, B.}, title = {Introduction to real-space renormalization-group methods in critical and chaotic phenomena}, journal = {Phys. Rep.}, year = {1982}, volume = {91}, pages = {233--295}, doi = {10.1016/0370-1573(82)90057-6}, } @Article{CrFaHu82, author = {Crutchfield, J. P. and Farmer, J. D. and Huberman, B. A.}, title = {Fluctuations and simple chaotic dynamics}, journal = {Phys. Rep.}, year = {1982}, volume = {92}, pages = {45--82}, doi = {10.1016/0370-1573(82)90089-8}, } @Article{Ott81, author = {Ott, E.}, title = {Strange attractors and chaotic motions of dynamical systems}, journal = {Rev. Mod. Phys.}, year = {1981}, volume = {53}, pages = {655--671}, doi = {10.1007/978-0-387-21830-4_9}, } @Article{RicLoh06, author = {Richter, P. H. and Lohse, D.}, journal = {Nonlin. Phen. Compl. Syst.}, title = {{Siegfried Grossmann}: the great man, our teacher}, year = {2006}, pages = {105--108}, volume = {9}, url = {http://ftp.camtp.uni-mb.si/fizmb/2010/GrossmannLaudatio.pdf}, } @Book{BDGGPZ01, title = {{Chance in Physics}}, publisher = {Springer}, year = {2001}, editor = {Bricmont, J. and Ghirardi, G. and D{\"u}rr, D. and Petruccione, F. and Galavotti, M. C. and Zanghi, N.}, address = {Berlin}, doi = {10.1007/3-540-44966-3}, } @Book{LivVul03, editor = {Livi, R. and Vulpiani, A.}, publisher = {Springer}, title = {{{The Kolmogorov} Legacy in Physics}}, year = {2003}, address = {Berlin}, doi = {10.1007/b93809}, } @Book{ChLeNi07, title = {{Kolmogorov's Heritage in Mathematics}}, publisher = {Springer}, year = {2007}, editor = {Charpentier, {\'{E}}. and Lesne, A. and Nikolski, N. K.}, address = {Berlin}, doi = {10.1007/978-3-540-36351-4}, } @Book{Sattinger79, title = {{Group Theoretic Methods in Bifurcation Theory}}, publisher = {Springer}, year = {1979}, author = {Sattinger, D. H.}, address = {Berlin}, doi = {10.1007/bfb0087456}, } @Book{BlChAn10, title = {{Applications of Symmetry Methods to Partial Differential Equations}}, publisher = {Springer}, year = {2010}, author = {Bluman, G. W. and Cheviakov, A. F. and Anco, S. C.}, address = {New York}, doi = {10.1007/978-0-387-68028-6}, } @Book{AusDir06, title = {{The Logistic Map and the Route to Chaos}}, publisher = {Springer}, year = {2006}, editor = {Ausloos, M. and Dirickx, M.}, address = {Berlin}, doi = {10.1007/3-540-32023-7}, } @Article{HubRud80, author = {Huberman, B. A. and Rudnick, J.}, title = {Scaling behavior of chaotic flows}, journal = {Phys. Rev. Lett.}, year = {1980}, volume = {45}, pages = {154--156}, doi = {10.1103/physrevlett.45.154}, } @Article{CFDPSJD80, author = {Crutchfield, J. and Farmer, D. and Packard, N. and Shaw, R. and Jones, G. and Donnelly, R. J.}, title = {Power spectral analysis of a dynamical system}, journal = {Phys. Lett. A}, year = {1980}, volume = {76}, pages = {1--4}, doi = {10.1016/0375-9601(80)90130-9}, } @Article{ShiNag79, author = {I. Shimada and T. Nagashima}, title = {A numerical approach to ergodic problem of dissipative dynamical systems}, journal = {Progr. Theor. Phys.}, year = {1979}, volume = {61}, pages = {1605--1616}, doi = {10.1143/ptp.61.1605}, } @InCollection{Chillingworth71, author = {Brunovsk{\'y}, P.}, title = {One-parameter families of dipheomorpisms}, booktitle = {{Proc. Symposium on Differential Equations and Dynamical Systems 68-69}}, publisher = {Springer}, year = {1971}, editor = {Chillingworth, D.}, address = {Berlin}, doi = {10.1007/bfb0070117}, } @Article{Lyubich99, author = {Lyubich, M.}, title = {{Feigenbaum-Coullet-Tresser} universality and {Milnor}'s hairiness conjecture}, journal = {Ann. Math.}, year = {1999}, volume = {149}, pages = {319--420}, doi = {10.2307/120968}, } @Article{Lyubich95, author = {M. Lyubich}, title = {Renormalization ideas in conformal dynamics}, journal = {Current Developments in Mathematics}, year = {1995}, volume = {1995}, pages = {155--190}, doi = {10.4310/cdm.1995.v1995.n1.a2}, } @Article{AubDal02, author = {Aubin, D. and Dalmedico, A. D.}, title = {Writing the history of dynamical systems and chaos: {Longue} dur{\'{e}}e and revolution, disciplines and cultures}, journal = {Historia Mathematica}, year = {2002}, volume = {29}, pages = {273--339}, doi = {10.1006/hmat.2002.2351}, } @InCollection{WaKo12, author = {G. M. Wadsworth and D. T. Kovari}, title = {Optimal resolution of state space in chaotic hyperbolic 2-dimensional maps}, booktitle = {{ChaosBook.org/projects}}, publisher = {Georgia Inst. of Technology}, year = {2012}, chapter = {Optimal resolution of state space in chaotic hyperbolic 2-dimensional maps}, url = {http://ChaosBook.org/projects/index.shtml#Kovari}, } @Article{UlaNeu47, author = {Ulam, S. and von Neumann, J.}, title = {On combination of stochastic and deterministic processes}, journal = {Bull. Amer. Math. Soc.}, year = {1947}, volume = {53}, pages = {1120}, } @Article{Thoo98, author = {Thoo, J. B.}, title = {A picture is worth a thousand words}, journal = {College Math. J.}, year = {1998}, volume = {29}, pages = {408--411}, doi = {10.2307/2687256}, } @Book{DayanAbbott01, title = {{Theoretical Neuroscience}}, publisher = {MIT Press}, year = {2001}, author = {Dayan, P. and Abbott, L. F.}, address = {Cambridge, MA}, } @Article{LiMa83, author = {Li, T.-P. and Ma, Y.-Q.}, title = {Analysis methods for results in gamma-ray astronomy}, journal = {Astrophys. J.}, year = {1983}, volume = {272}, pages = {317--324}, doi = {10.1086/161295}, } @Article{FelCou98, author = {Feldman, G. J. and Cousins, R. D.}, title = {Unified approach to the classical statistical analysis of small signals}, journal = {Phys. Rev. D}, year = {1998}, volume = {57}, pages = {3873--3889}, doi = {10.1103/PhysRevD.57.3873}, } @Article{Lyons13, author = {Lyons, L.}, journal = {Contemporary Physics}, title = {{Bayes and Frequentism}: a particle physicist's perspective}, year = {2013}, pages = {1--16}, volume = {54}, abstract = {In almost every scientific field, an experiment involves collecting data and then analysing it. The analysis stage will often consist in trying to extract some physical parameter and estimating its uncertainty; this is known as Parameter Determination. An example would be the determination of the mass of the top quark, from data collected from high energy proton--proton collisions. A different aim is to choose between two possible hypotheses. For example, are data on the recession speed s of distant galaxies proportional to their distance d, or do they fit better to a model where the expansion of the Universe is accelerating? There are two fundamental approaches to such statistical analyses -- Bayesian and Frequentist. This article discusses the way they differ in their approach to probability, and then goes on to consider how this affects the way they deal with Parameter Determination and Hypothesis Testing. The examples are taken from everyday life and from particle physics.}, doi = {10.1080/00107514.2012.756312}, } @Misc{Willis19, author = {Willis, A. P.}, title = {Equilibria, periodic orbits and computing them}, year = {2019}, eprint = {1908.06730}, eprinttype = {arxiv}, } @Article{DonLiu19, author = {Dong, C. and Liu, H.}, title = {Analysis of periodic orbits for the {Chen} and the {L{\"u}} systems via a variational approach}, journal = {J. Korean Phys. Soc.}, year = {2019}, volume = {75}, pages = {188--195}, doi = {10.3938/jkps.75.188}, } @Article{DonJia19, author = {Dong, C. and Jia, L.}, title = {Periodic orbits analysis for the {Zhou} system via variational approach}, journal = {Mod. Phys. Lett. B}, year = {2019}, volume = {33}, pages = {1950212}, doi = {10.1142/s0217984919502129}, } @InCollection{statespDummies, author = {Cvitanovi{\'c}, P.}, title = {Life in extreme dimensions}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2020}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/paper.shtml#flows}, } @Article{ShuIke16, author = {Shudo, A. and Ikeda, K. S.}, title = {Toward pruning theory of the {Stokes} geometry for the quantum {H{\'{e}}non} map}, journal = {Nonlinearity}, year = {2016}, volume = {29}, pages = {375--425}, doi = {10.1088/0951-7715/29/2/375}, } @Book{Ahlfors53, author = {Ahlfors, L. V.}, publisher = {Mc Graw Hill}, title = {{Complex Analysis}}, year = {1979}, edition = {3}, isbn = {9780070006577}, } @Book{Needham97, author = {Needham, T.}, publisher = {Oxford Univ. Press}, title = {{Visual Complex Analysis}}, year = {1997}, address = {Oxford UK}, isbn = {9780198534464}, doi = {10.2307/3618747}, } @Article{DonLiu19a, author = {Dong, C. and Liu, H.}, title = {Unstable cycles for the {Burke-Shaw} system via variational approach}, journal = {Int. J. Mod. Phys. B}, year = {2019}, volume = {33}, pages = {1950240}, doi = {10.1142/s0217979219502400}, } @Article{PaSpVi07, author = {Panchev, S. and Spassova, T. and Vitanov, N. K.}, title = {Analytical and numerical investigation of two families of {Lorenz}-like dynamical systems}, journal = {Chaos Solit. Fract.}, year = {2007}, volume = {33}, pages = {1658--1671}, doi = {10.1016/j.chaos.2006.03.037}, } @Article{LDRG96, author = {Letellier, C. and Dutertre, P. and Reizner, J. and Gouesbet, G.}, title = {Evolution of a multimodal map induced by an equivariant vector field}, journal = {J. Phys. A}, year = {1996}, volume = {29}, pages = {5359--5373}, doi = {10.1088/0305-4470/29/17/012}, } @Article{BaFaWe14, author = {Barkhofen, S. and Faure, F. and Weich, T.}, title = {Resonance chains in open systems, generalized zeta functions and clustering of the length spectrum}, journal = {Nonlinearity}, year = {2014}, volume = {27}, pages = {1829--1858}, doi = {10.1088/0951-7715/27/8/1829}, } @Book{Elaydi05, title = {{An Introduction to Difference Equations}}, publisher = {Springer}, year = {2005}, author = {Elaydi, S.}, address = {Berlin}, doi = {10.1007/0-387-27602-5}, } @Article{RagZad52, author = {Ragazzini, J. R. and Zadeh, L. A.}, title = {The analysis of sampled-data systems}, journal = {Trans. AIEE}, year = {1952}, volume = {71}, pages = {225--234}, doi = {10.1109/tai.1952.6371274}, } @InCollection{Hurewicz47, author = {W. Hurewicz}, title = {Filters and servo systems with pulsed data}, booktitle = {{Theory of Servomechanisms}}, publisher = {McGraw-Hill}, year = {1947}, editor = {James, H. M. and Nichols, N. B. and Phillips, R. S.}, pages = {231--261}, address = {New York}, url = {https://catalog.hathitrust.org/api/volumes/oclc/2591852.html}, } @Book{Polya54I, title = {{Mathematics and Plausible Reasoning, Vol. 1 Induction and Analogy in Mathematics}}, publisher = {Princeton Univ. Press}, year = {1954}, author = {Polya, G.}, isbn = {9780691025094}, } @InCollection{HopWil07, author = {Hopkins, B. and Wilson, R.}, title = {Euler's science of combinations}, booktitle = {{Leonhard Euler: Life, Work and Legacy}}, publisher = {Elsevier}, year = {2007}, editor = {Bradley, R. E. and Sandifer, C. E.}, pages = {395--408}, url = {https://www.gss.ucsb.edu/sites/secure.lsit.ucsb.edu.germ.d7/files/sitefiles/news/conferences/euler/Hopkins2.pdf}, } @Article{Jury54, author = {Jury, E. I.}, journal = {Trans. AIEE}, title = {Analysis and synthesis of sampled-data control systems}, year = {1954}, pages = {332--346}, volume = {73}, doi = {10.1109/tce.1954.6372164}, } @Article{HaShTa99, author = {Harayama, T. and Shudo, A. and Tasaki, S.}, title = {Semiclassical {Fredholm} determinant for strongly chaotic billiards}, journal = {Nonlinearity}, year = {1999}, volume = {12}, pages = {1113--1149}, doi = {10.1088/0951-7715/12/4/322}, } @Article{MMWS98, author = {Main, J. and Mandelshtam, Vl. A. and Wunner, G. and Taylor, H. S.}, title = {Harmonic inversion as a general method for periodic orbit quantization}, journal = {Nonlinearity}, year = {1998}, volume = {11}, pages = {1015--1035}, doi = {10.1088/0951-7715/11/4/014}, } @Article{Bruns1887, author = {H. Bruns}, title = {{{\"U}ber die Integrale des Vielk{\"o}rper-Problems}}, journal = {Acta Math.}, year = {1887}, volume = {11}, pages = {25--96}, doi = {10.1007/bf02612319}, } @Article{CHPS18, author = {C{\'{o}}rdova, C. and Heidenreich, B. and Popolitov, A. and Shakirov, S.}, title = {Orbifolds and exact solutions of strongly-coupled matrix models}, journal = {Commun Math Phys}, year = {2018}, volume = {361}, pages = {1235--1274}, doi = {10.1007/s00220-017-3072-x}, } @InProceedings{GalTuc09, author = {Galias, Z. and Tucker, W.}, booktitle = {2009 {IEEE} Intern. Symp. Circuits and Systems}, title = {Symbolic dynamics based method for rigorous study of the existence of short cycles for chaotic systems}, year = {2009}, pages = {1907--1910}, publisher = {{IEEE}}, doi = {10.1109/iscas.2009.5118153}, url = {https://www.researchgate.net/profile/Warwick_Tucker}, } @Article{GPNESM18, author = {Gallego, J. A. and Perich, M. G. and Naufel, S. N. and Ethier, C. and Solla, S. A. and Miller, L. E.}, title = {Cortical population activity within a preserved neural manifold underlies multiple motor behaviors}, journal = {Nat. Commun.}, year = {2018}, volume = {9}, pages = {4233}, doi = {10.1038/s41467-018-06560-z}, } @Article{GPCSM18, author = {Gallego, J. A. and Perich, M. G. and Chowdhury, R. H. and Solla, S. A. and Miller, L. E.}, journal = {Nature Neuroscience}, title = {Long-term stability of cortical population dynamics underlying consistent behavior}, year = {2020}, pages = {260--270}, volume = {23}, doi = {10.1038/s41593-019-0555-4}, } @InProceedings{FGCBMS19, author = {Farshchian, A. and Gallego, J. A. and Cohen, J. P. and Bengio, Y. and Miller, L. E. and Solla, S. A.}, title = {Adversarial domain adaptation for stable brain-machine interfaces}, booktitle = {{International Conference on Learning Representations}}, year = {2019}, pages = {1--14}, url = {https://openreview.net/forum?id=Hyx6Bi0qYm}, } @Article{Doedel97, author = {Doedel, E. J.}, title = {Nonlinear numerics}, journal = {J. Franklin Inst.}, year = {1997}, volume = {334}, pages = {1049--1073}, doi = {10.1016/s0016-0032(97)00027-6}, } @Article{BarBle09, author = {Barrio, R. and Blesa, F.}, title = {Systematic search of symmetric periodic orbits in {2DOF Hamiltonian} systems}, journal = {Chaos Solit. Fract.}, year = {2009}, volume = {41}, pages = {560--582}, doi = {10.1016/j.chaos.2008.02.032}, } @Article{WuSche06, author = {Wulff, C. and Schebesch, A.}, title = {Numerical continuation of symmetric periodic orbits}, journal = {SIAM J. Appl. Dyn. Syst.}, year = {2006}, volume = {5}, pages = {435--475}, doi = {10.1137/050637170}, } @Article{WalRic19, author = {Waltner, D. and Richter, K.}, title = {Towards a semiclassical understanding of chaotic single- and many-particle quantum dynamics at post-{Heisenberg} time scales}, journal = {Phys. Rev. E}, year = {2019}, volume = {100}, number = {042212}, doi = {10.1103/physreve.100.042212}, } @Article{GHJSC16, author = {Gutkin, B. and Han, L. and Jafari, R. and Saremi, A. K. and Cvitanovi{\'c}, P.}, journal = {Nonlinearity}, title = {Linear encoding of the spatiotemporal cat}, year = {2021}, pages = {2800--2836}, volume = {34}, doi = {10.1088/1361-6544/abd7c8}, } @Misc{CL18, author = {P. Cvitanovi{\'c} and H. Liang}, note = {In preparation}, title = {Spatiotemporal cat: {An} exact classical chaotic field theory}, year = {2019}, url = {https://arxiv.org/abs/2201.11325}, } @Article{KuGuKu19, author = {Kuipers, F. and G{\"u}rsoy, U. and Kuznetsov, Y.}, journal = {J. High Energy Phys.}, title = {Bifurcations in the {RG}-flow of {QCD}}, year = {2019}, pages = {075}, volume = {2019}, doi = {10.1007/jhep07(2019)075}, } @Book{KapGla95, title = {{Understanding Nonlinear Dynamics}}, publisher = {Springer}, year = {1995}, author = {Kaplan, D. and Glass, L.}, address = {New York}, doi = {10.1007/978-1-4612-0823-5}, } @Article{WeeHar88, author = {Weeks, D. E. and Harter, W. G.}, title = {Vibrational frequencies and normal modes of buckminsterfullerene}, journal = {Chem. Phys. Lett.}, year = {1988}, volume = {144}, pages = {366--372}, doi = {10.1016/0009-2614(88)87130-6}, } @Article{LiTom19b, author = {Li, J. and Tomsovic, S.}, title = {Asymptotic relationship between homoclinic points and periodic orbit stability exponents}, journal = {Phys. Rev. E}, year = {2019}, volume = {100}, number = {052202}, doi = {10.1103/physreve.100.052202}, } @Book{CeCeVu09, title = {{Chaos: From Simple Models to Complex Systems}}, publisher = {World Scientific}, year = {2009}, author = {Cencini, M. and Cecconi, F. and Vulpiani, A.}, address = {Singapore}, doi = {10.1142/7351}, } @Book{AFHF15, title = {{An Exploration of Dynamical Systems and Chaos}}, publisher = {Springer}, year = {2015}, author = {Argyris, J. H. and Faust, G. and Haase, M. and Friedrich, R.}, address = {Berlin}, doi = {10.1007/978-3-662-46042-9}, } @Article{ZapFli19, author = {Zaporski, L. and Flicker, F.}, title = {Superconvergence of topological entropy in the symbolic dynamics of substitution sequences}, journal = {{SciPost} Physics}, year = {2019}, volume = {7}, pages = {018}, doi = {10.21468/scipostphys.7.2.018}, } @Article{Yampolsky03, author = {Yampolsky, M.}, title = {Hyperbolicity of renormalization of critical circle maps}, journal = {Publ. Math. IHES}, year = {2003}, volume = {96}, pages = {1--41}, publisher = {IHES}, url = {http://eudml.org/doc/104187}, } @Book{Bullo19, author = {F. Bullo}, publisher = {Kindle Direct Publishing}, title = {{Lectures on Network Systems}}, year = {2019}, isbn = {978-1986425643}, note = {With contributions by J. Cortes, F. Dorfler, and S. Martinez}, url = {http://motion.me.ucsb.edu/book-lns}, } @Article{AhCoSt19, author = {Ahamed, T. and Costa, A. C. and Stephens, G. J.}, title = {Capturing the continuous complexity of behavior in {C.} elegans}, journal = {bioRxiv}, year = {2019}, doi = {10.1101/827535}, publisher = {Cold Spring Harbor Laboratory}, } @Article{Galias19, author = {Galias, Z.}, title = {On topological entropy of finite representations of the {H{\'{e}}non} map}, journal = {Int. J. Bifurcation Chaos}, year = {2019}, volume = {29}, pages = {1950175}, doi = {10.1142/s021812741950175x}, } @Article{GalTuc15, author = {Galias, Z. and Tucker, W.}, title = {Is the {H{\'{e}}non} attractor chaotic?}, journal = {Chaos}, year = {2015}, volume = {25}, pages = {033102}, doi = {10.1063/1.4913945}, } @Article{Bowen71a, author = {Bowen, R.}, journal = {Trans. Amer. Math. Soc.}, title = {Entropy for group endomorphisms and homogeneous spaces}, year = {1971}, pages = {401--401}, volume = {153}, doi = {10.1090/s0002-9947-1971-0274707-x}, } @Article{LucGri19, author = {Lucarini, V. and Gritsun, A.}, title = {A new mathematical framework for atmospheric blocking events}, journal = {Climate Dynamics}, year = {2019}, volume = {54}, pages = {1--24}, doi = {10.1007/s00382-019-05018-2}, } @Article{Campbell15, author = {Campbell, D. K.}, title = {Editorial: The pre-history of {Chaos-An Interdisciplinary Journal of Nonlinear Science}}, journal = {Chaos}, year = {2015}, volume = {25}, pages = {090401}, doi = {10.1063/1.4928745}, } @InCollection{CBgetused, author = {P. Cvitanovi{\'c}}, title = {Why cycle?}, booktitle = {{Chaos: Classical and Quantum}}, publisher = {Niels Bohr Inst.}, year = {2020}, editor = {P. Cvitanovi{\'c} and R. Artuso and R. Mainieri and G. Tanner and G. Vattay}, address = {Copenhagen}, url = {http://ChaosBook.org/paper.shtml#getused}, } @Book{YutsisLevVan62, title = {{The Theory of Angular Momentum}}, publisher = {Gordon and Breach}, year = {1964}, author = {Yutsis, A. P. and Levinson, I. B. and Vanagas, V. V.}, address = {New York}, } @Book{LinMor82, title = {{Atomic Many-Body Theory}}, publisher = {Springer}, year = {1982}, author = {Lindgren, I. and Morrison, J.}, address = {Berlin}, doi = {10.1007/978-3-642-96614-9}, } @Book{VaMoKh88, title = {{Quantum Theory of Angular Momentum}}, publisher = {World Scientific}, year = {1988}, author = {Varshalovich, D. A. and Moskalev, A. N. and Khersonskii, V. K.}, address = {Singapore}, doi = {10.1142/0270}, } @Book{Judd63, title = {{Operator Techniquesin Atomic Spectroscopy}}, publisher = {Princeton Univ. Press}, year = {1963}, author = {Judd, B. R.}, url = {https://catalog.hathitrust.org/Record/000621355}, } @Book{FowMcG19, title = {{Chaos: An Introduction for Applied Mathematicians}}, publisher = {Springer}, year = {2019}, author = {Fowler, A. and McGuinness, M.}, address = {Berlin}, doi = {10.1007/978-3-030-32538-1}, } @Misc{LinGra20, author = {Linot, A. J. and Graham, M. D.}, title = {Deep learning to discover and predict dynamics on an inertial manifold}, year = {2020}, eprint = {2001.04263}, eprinttype = {arxiv}, } @Article{AkHaRa20, author = {Akram, M. and Hassanaly, M. and Raman, V.}, journal = {J. Comp. Phys.}, title = {A priori analysis of reduced description of dynamical systems using approximate inertial manifolds}, year = {2020}, pages = {109344}, volume = {409}, doi = {10.1016/j.jcp.2020.109344}, } @InCollection{Veen18, author = {van Veen, L.}, booktitle = {{Computational Methods in Applied Sciences}}, publisher = {Springer}, title = {A brief history of simple invariant solutions in turbulence}, year = {2018}, pages = {217--231}, doi = {10.1007/978-3-319-91494-7_7}, } @article{Doedel81, author = {Doedel, E. J.}, year = {1981}, title = {{AUTO}: a program for the automatic bifurcation analysis for autonomous systems}, journal = {Congressus Numerantium}, volume = {30}, pages = {265-284}, } @TechReport{auto, author = {Doedel, E. J. and Champneys, A. R. and Fairgrieve, T. F. and Kuznetsov, Y. A. and Sandstede, B. and Wang, X.}, institution = {Computational Mathematics and Visualization Laboratory, Concordia Univ.}, title = {{AUTO: Continuation and Bifurcation Software for Ordinary Differential Equations}}, year = {2007}, url = {http://indy.cs.concordia.ca/auto/}, } @TechReport{Doedel10, author = {Doedel, E. J.}, institution = {Concordia Univ.}, title = {{Lecture Notes on Numerical Analysis of Nonlinear Equations}}, year = {2010}, url = {http://indy.cs.concordia.ca/auto/notes.pdf}, } @Article{CLGC20, author = {Cerbus, R. T. and Liu, C.-c. and Gioia, G. and Chakraborty, P.}, journal = {Sci. Adv.}, title = {Small-scale universality in the spectral structure of transitional pipe flows}, year = {2020}, pages = {eaaw6256}, volume = {6}, doi = {10.1126/sciadv.aaw6256}, } @Article{WuZaMe20, author = {Wu, Z. and Zaki, T. A. and Meneveau, C.}, journal = {Proc. Natl. Acad. Sci.}, title = {{High-Reynolds}-number fractal signature of nascent turbulence during transition}, year = {2020}, pages = {3461--3468}, volume = {117}, doi = {10.1073/pnas.1916636117}, } @Article{AvHo2013, Title = {Nature of laminar-turbulence intermittency in shear flows}, Author = {Avila, M. and Hof, B.}, Journal = {Phys. Rev. E}, Year = {2013}, Pages = {063012}, Volume = {87}, DOI = {10.1103/PhysRevE.87.063012}, } @Article{BSMLAH15, Title = {The rise of fully turbulent flow}, Author = {Barkley, D. and Song, B. and Mukund, V. and Lemoult, G. and Avila, M. and Hof, B.}, Journal = {Nature}, Year = {2015}, Pages = {550--553}, Volume = {526}, DOI = {10.1038/nature15701} } @TechReport{Cliffe96, AUTHOR = {Cliffe, K. A.}, TITLE = {{ENTWIFE} (release 6.3) reference manual}, YEAR = {1996}, institution = {Oxford, {UK}: {Harwell Laboratory}}, url = {http://www.swmath.org/software/4255}, } @Article{CliMul85, author = {Cliffe, K. A. and Mullin, T.}, journal = {J. Fluid Mech.}, title = {A numerical and experimental study of anomalous modes in the {Taylor} experiment}, year = {1985}, pages = {243-258}, volume = {153}, doi = {10.1017/s0022112085001240}, } @InProceedings{Tuckerman89, author = {Tuckerman, L. S.}, booktitle = {{Proc. XI Intern. Conf. Numerical Methods in Fluid Dynamics}}, title = {Steady state solving via {Stokes} preconditioning -- recursion relations for elliptic operators}, year = {1989}, editor = {Dwoyer, D. L. and Hussaini, M. Y. and Voigt, R. G.}, pages = {573--577}, publisher = {Springer}, } @Article{SYE05, author = {J. D. Skufca and J. A. Yorke and B. Eckhardt}, journal = {Phys. Rev. Lett.}, title = {{Edge of Chaos} in a parallel shear flow}, year = {2006}, pages = {174101}, volume = {96}, doi = {10.1103/PhysRevLett.96.174101}, } @Article{TI03, author = {S. Toh and T. Itano}, journal = {J. Fluid Mech.}, title = {A periodic-like solution in channel flow}, year = {2003}, pages = {67--76}, volume = {481}, doi = {10.1017/s0022112003003768}, } @Article{LucKer14, author = {Lucas, D. and Kerswell, R. R.}, journal = {Phys. Fluids}, title = {Recurrent flow analysis in spatiotemporally chaotic 2-dimensional {Kolmogorov} flow}, year = {2015}, pages = {518--554}, volume = {27}, doi = {10.1063/1.4917279}, } @Article{KKSDEH16, author = {T. Khapko and T. Kreilos and P. Schlatter and Y. Duguet and B. Eckhardt and D. S. Henningson}, journal = {J. Fluid Mech.}, title = {Edge states as mediators of bypass transition in boundary-layer flows}, year = {2016}, pages = {R2}, volume = {801}, doi = {10.1017/jfm.2016.434}, } @Article{VaVeKa18, author = {van Veen, L. and Vela-Mart{\'i}n, A. and Kawahara, G.}, journal = {Phys. Rev. Lett.}, title = {Time-periodic inertial range dynamics}, year = {2019}, pages = {134502}, volume = {123}, doi = {10.1103/physrevlett.123.134502}, } @Article{SNGS, author = {S{\'a}nchez, J. and Net, M. and Garc{\'i}a-{A}rchilla, B. and Sim{\'o}, C.}, journal = {J. Comp. Phys.}, title = {{Newton-Krylov} continuation of periodic orbits for {Navier-Stokes} flows}, year = {2004}, pages = {13--33}, volume = {201}, doi = {10.1016/j.jcp.2004.04.018}, } @Article{KDKSEH14, author = {Khapko, T. and Duguet, Y. and Kreilos, T. and Schlatter, P. and Eckhardt, B. and Henningson, D. S.}, journal = {Eur. Phys. J. E}, title = {Complexity of localised coherent structures in a boundary-layer flow}, year = {2014}, pages = {32}, volume = {37}, doi = {10.1140/epje/i2014-14032-3}, } @InProceedings{ZhaWei19, author = {Zhang, W. and Wei, M.}, booktitle = {{{AIAA} Scitech 2019 Forum}}, title = {Solving generalized eigenvalue problem: an alternative approach for dynamic mode decomposition}, year = {2019}, publisher = {American Inst. Aeronautics and Astronautics}, doi = {10.2514/6.2019-1897}, } @Article{Bagheri13, Title = {Koopman-mode decomposition of the cylinder wake}, Author = {Bagheri, S.}, Journal = {J. Fluid Mech.}, Year = {2013}, Pages = {596--623}, Volume = {726}, DOI = {10.1017/jfm.2013.249} } @InCollection{Pazy83, author = {A. Pazy}, booktitle = {{Lecture Notes Math.}}, publisher = {Springer}, title = {Semigroups of operators in {Banach} spaces}, year = {1983}, address = {Berlin}, pages = {508--524}, doi = {10.1007/bfb0103275}, } @Article{KotSun00, author = {Kotani, M. and Sunada, T.}, journal = {J. Math. Sci. Univ. Tokyo}, title = {Zeta functions of finite graphs}, year = {2000}, pages = {7--25}, volume = {7}, url = {https://ci.nii.ac.jp/naid/110000071386/}, } @Article{Bass92, Title = {The {Ihara-Selberg} zeta function of a tree lattice}, Author = {H. Bass}, Journal = {Int. J. Math.}, Year = {1992}, Pages = {717--797}, Volume = {3}, DOI = {10.1142/S0129167X92000357} } @Article{Hashimoto89, Title = {Zeta functions of finite graphs and representations of p-adic groups}, Author = {Hashimoto, K.}, Journal = {Adv. Stud. Pure Math.}, Year = {1989}, Pages = {211--280}, Volume = {15}, DOI = {10.1016/B978-0-12-330580-0.50015-X} } @Article{StaTer96, author = {Stark, H. M. and Terras, A. A.}, journal = {Adv. Math.}, title = {Zeta functions of finite graphs and coverings}, year = {1996}, pages = {124--165}, volume = {121}, doi = {10.1006/aima.1996.0050}, } @Article{StaTer00, author = {Stark, H. M. and Terras, A. A.}, journal = {Adv. Math.}, title = {Zeta functions of finite graphs and coverings, {Part II}}, year = {2000}, pages = {132--195}, volume = {154}, doi = {10.1006/aima.2000.1917}, } @Book{Serre80, author = {Serre, J.-P.}, publisher = {Springer}, title = {{Trees}}, year = {1980}, address = {Berlin}, doi = {10.1007/978-3-642-61856-7}, } @Article{Sunada89, author = {Sunada, T.}, journal = {Topology}, title = {Unitary representations of fundamental groups and the spectrum of twisted {Laplacians}}, year = {1989}, pages = {125--132}, volume = {28}, doi = {10.1016/0040-9383(89)90015-3}, } @Article{HuaLaii20, author = {Huang, L. and Lai, Y.-C.}, journal = {Commun. Theor. Phys.}, title = {Perspectives on relativistic quantum chaos}, year = {2020}, pages = {047601}, volume = {72}, doi = {10.1088/1572-9494/ab6909}, } @Article{ChJoKa14, author = {Chinta, G. and Jorgenson, J. and Karlsson, A.}, journal = {Monatsh. Math.}, title = {Heat kernels on regular graphs and generalized {Ihara} zeta function formulas}, year = {2014}, pages = {171--190}, volume = {178}, doi = {10.1007/s00605-014-0685-4}, } @Article{focusPOT, Title = {Recurrent flows: the clockwork behind turbulence}, Author = {Cvitanovi{\'c}, P.}, Journal = {J. Fluid Mech. Focus Fluids}, Year = {2013}, Pages = {1--4}, Volume = {726}, DOI = {10.1017/jfm.2013.198} } @Article{Lan10, author = {Y. Lan}, journal = {Commun. Nonlinear Sci. Numer. Simul.}, pages = {502--526}, title = {Cycle expansions: {From} maps to turbulence}, volume = {15}, year = {2010}, doi = {10.1016/j.cnsns.2009.04.022}, } @Article{yorke2, author = {C. Grebogi and E. Ott and J. A. Yorke}, journal = {Phys. Rev. A}, pages = {1711--1724}, title = {Unstable periodic orbits and the dimensions of multifractal chaotic attractors}, volume = {37}, year = {1988}, doi = {10.1103/PhysRevA.37.1711}, } @Article{kostelich97, author = {E. J. Kostelich and I. Kan and C. Grebogi and E. Ott and J. A. Yorke}, journal = {Physica D}, pages = {81--90}, title = {Unstable dimension variability: a source of nonhyperbolicity in chaotic systems}, volume = {109}, year = {1997}, doi = {10.1016/s0167-2789(97)00161-9}, } @Article{PawSchu91, author = {K. Pawelzik and H. G. Schuster}, journal = {Phys. Rev. A}, pages = {1808--1812}, title = {Unstable periodic orbits and prediction}, volume = {43}, year = {1991}, doi = {10.1103/PhysRevA.43.1808}, } @Article{Zoldi98, author = {S. M. Zoldi}, journal = {Phys. Rev. Lett.}, pages = {3375--3378}, title = {Unstable periodic orbits analysis of histograms of chaotic time series}, volume = {81}, year = {1998}, doi = {10.1103/physrevlett.81.3375}, } @Misc{Zoldi99, author = {S. M. Zoldi}, title = {Escape time weighting of unstable stationary solutions of spatiotemporal chaos}, year = {1999}, url = {http://arXiv.org/abs/chao-dyn/9903020}, } @Article{KeTu06, author = {Kerswell, R. R. and Tutty, O. R.}, journal = {J. Fluid Mech.}, title = {Recurrence of travelling waves in transitional pipe flow}, year = {2007}, pages = {69--102}, volume = {584}, doi = {10.1017/s0022112007006301}, } @Article{ChaDeVore79, author = {J. G. Charney and J. G. DeVore}, journal = {J. Meteorology}, pages = {1205--1216}, title = {Multiple flow equilibria in the atmosphere and blocking}, volume = {36}, year = {1979}, doi = {10.1175/1520-0469(1979)036<1205:MFEITA>2.0.CO;2}, } @Article{Gritsun10, author = {Gritsun, A.}, journal = {Dokl. Earth Sciences}, pages = {1688--1691}, title = {Statistical characteristics of barotropic atmospeheric system and its unstable periodic solutions}, volume = {435}, year = {2010}, doi = {10.1134/S1028334X10120287}, } @Article{Gritsun11, author = {Gritsun, A.}, journal = {Dokl. Earth Sciences}, pages = {636--640}, title = {Connection of periodic orbits and variability patterns of circulation for the barotropic model of atmospheric dynamics}, volume = {438}, year = {2011}, doi = {10.1134/S1028334X11050035}, } @Article{Gritsun13, author = {Gritsun, A.}, journal = {Philos. Trans. Royal Soc. A}, title = {Statistical characteristics, circulation regimes and unstable periodic orbits of a barotropic atmospheric model}, volume = {371}, year = {2013}, doi = {10.1098/rsta.2012.0336}, } @Article{GrBrMa08, author = {A. Gritsun and G. Branstator and A. Majda}, journal = {J. Atmos. Sci.}, pages = {2824--2841}, title = {Climate response of linear and quadratic functionals using the fluctuation-dissipation theorem}, volume = {65}, year = {2008}, doi = {10.1175/2007JAS2496.1}, } @Article{SelBran04, author = {F. M. Selten and G. Branstator}, journal = {J. Atmos. Sci.}, pages = {2267--2282}, title = {Preferred regime transition routes and evidence for an unstable periodic orbit in a baroclinic model}, volume = {61}, year = {2004}, doi = {10.1175/1520-0469(2004)061<2267:PRTRAE>2.0.CO;2}, } @Article{HaiMaj10, author = {M. Hairer and A. J. Majda}, journal = {Nonlinearity}, pages = {909--922}, title = {A simple framework to justify linear response theory}, volume = {23}, year = {2010}, doi = {10.1088/0951-7715/23/4/008}, } @Article{AbrMaj08, author = {Abramov, R. V. and Majda, A. J.}, journal = {J. Nonlin. Sci.}, pages = {303--341}, title = {New approximations and tests of linear fluctuation-response for chaotic nonlinear forced-dissipative dynamical systems}, volume = {18}, year = {2008}, doi = {10.1007/s00332-007-9011-9}, } @Article{Abramov09, author = {R. V. Abramov}, journal = {Chin. Ann. Math.}, pages = {447--462}, title = {Short-time linear response with reduced-rank tangent map}, volume = {30}, year = {2009}, doi = {10.1007/s11401-009-0088-3}, } @Misc{Goldobin12, author = {Goldobin, D. S.}, title = {Limit distribution of averages over unstable periodic orbits forming chaotic attractor}, year = {2012}, url = {http://arXiv.org/abs/1208.1691}, } @Article{KaiTom80, author = {T. Kai and K. Tomita}, journal = {Progr. Theor. Phys.}, pages = {1532--1550}, title = {Statistical mechanics of deterministic chaos}, volume = {64}, year = {1980}, doi = {10.1143/PTP.64.1532}, } @PhdThesis{hansen, author = {Hansen, K. T.}, school = {Univ. of Oslo}, title = {{Symbolic Dynamics in Chaotic Systems}}, year = {1993}, address = {Oslo, Norway}, url = {http://ChaosBook.org/projects/KTHansen/thesis}, } @Article{Lai97, author = {Y.-C. Lai}, journal = {Phys. Rev. E}, pages = {6531--6539}, title = {Characterization of the natural measure by unstable periodic orbits in nonhyperbolic chaotic systems}, volume = {56}, year = {1997}, doi = {10.1103/PhysRevE.56.6531}, } @Article{DhaLai99, author = {Dhamala, M. and Lai, Y.-C.}, journal = {Phys. Rev. E}, pages = {6176--6179}, title = {Unstable periodic orbits and the natural measure of nonhyperbolic chaotic saddles}, volume = {60}, year = {1999}, doi = {10.1103/PhysRevE.60.6176}, } @Article{ZakGol10, author = {Zaks, M. A. and Goldobin, D. S.}, journal = {Phys. Rev. E}, pages = {018201}, title = {Comment on ``{Time-averaged} properties of unstable periodic orbits and chaotic orbits in ordinary differential equation systems''}, volume = {81}, year = {2010}, doi = {10.1103/PhysRevE.81.018201}, } @Article{SaiYam98, author = {Saiki, Y. and Yamada, M.}, journal = {Nonlin. Proc. Geophys.}, pages = {675--680}, title = {Time averaged properties along unstable periodic orbits and chaotic orbits in two map systems}, volume = {15}, year = {2008}, doi = {10.5194/npg-15-675-2008}, } @Article{ReCi05, author = {Rempel, E. L. and Chian, A. C.}, journal = {Phys. Rev. E}, pages = {016203}, title = {Intermittency induced by attractor-merging crisis in the {Kuramoto-Sivashinsky} equation}, volume = {71}, year = {2005}, doi = {10.1103/PhysRevE.71.016203}, } @Article{Gritsun08, author = {Gritsun, A. S.}, journal = {Russian J. Numer. Analysis and Math. Modelling}, pages = {345--367}, title = {Unstable periodic trajectories of a barotropic model of the atmosphere}, volume = {23}, year = {2008}, doi = {10.1515/RJNAMM.2008.021}, } @Book{Gas97, author = {P. Gaspard}, publisher = {Cambridge Univ. Press}, title = {{Chaos, Scattering and Statistical Mechanics}}, year = {1997}, address = {Cambridge}, isbn = {9780521018258}, } @Article{CanDur04, author = {Cano, B. and Dur{\'a}n, A.}, journal = {{BIT} Numerical Mathematics}, pages = {215--235}, title = {A technique to improve the error propagation when integrating relative equilibria}, volume = {44}, year = {2004}, doi = {10.1023/b:bitn.0000039391.19365.56}, } @Article{DurSan98, author = {Dur{\'{a}}n, A. and Sanz-Serna, J. M.}, journal = {Nonlinearity}, pages = {1547--1567}, title = {The numerical integration of relative equilibrium solutions. {Geometric} theory}, volume = {11}, year = {1998}, doi = {10.1088/0951-7715/11/6/008}, } @Book{HaLuWa06, author = {Hairer, E. and Lubich, C. and Wanner, G.}, publisher = {Springer}, title = {{Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations}}, year = {2006}, address = {Berlin}, edition = {2}, doi = {10.1007/3-540-30666-8}, } @Article{Liao09, author = {Liao, S. J.}, journal = {Tellus A}, pages = {550--564}, title = {On the reliability of computed chaotic solutions of non-linear differential equations}, volume = {61}, year = {2009}, doi = {10.3402/tellusa.v61i4.15610}, } @Article{WaLiLi11, author = {Wang, P. F. and Li, J. P. and Li, Q.}, journal = {Numerical Algorithms}, pages = {147--159}, title = {Computational uncertainty and the application of a high-performance multiple precision scheme to obtaining the correct reference solution of {Lorenz} equations}, volume = {59}, year = {2011}, doi = {10.1007/s11075-011-9481-6}, } @Article{Liao11, author = {Liao, S. J.}, journal = {Commun. Nonlinear Sci. Numer. Simul.}, pages = {2564--2569}, title = {Chaos: {A} bridge from microscopic uncertainty to macroscopic randomness}, volume = {17}, year = {2011}, doi = {10.1016/j.cnsns.2011.10.033}, } @Article{Liao11a, author = {Liao, S. J.}, journal = {Chaos Solit. Fract.}, title = {On the numerical simulation of propagation of micro-level uncertainty for chaotic dynamic systems}, year = {2013}, volume = {47}, doi = {10.1016/j.chaos.2012.11.009}, } @Article{KlBo011, author = {A. Klebanoff and E. Bollt}, journal = {Chaos Solit. Fract.}, pages = {1305--1322}, title = {Convergence analysis of {Davidchack and Lai's} algorithm for finding periodic orbits}, volume = {12}, year = {2001}, doi = {10.1016/S0960-0779(00)00099-0}, } @Article{ChoGuck99, author = {W. G. Choe and J. Guckenheimer}, journal = {Computer Meth. Appl. Mech. and Engin.}, pages = {331--341}, title = {Computing periodic orbits with high accuracy}, volume = {170}, year = {1999}, doi = {10.1016/S0045-7825(98)00201-1}, } @Article{OlVa94, author = {A. Olvera and C. Vargas}, journal = {Physica D}, pages = {351--371}, title = {A continuation method to study periodic orbits of the {Froeschl\'e} map}, volume = {72}, year = {1994}, doi = {10.1016/0167-2789(94)90238-0}, } @Article{LiMaFeCh10, author = {Lin, W. and Ma, H. and Feng, J. and Chen, G.}, journal = {Phys. Rev. E}, pages = {046214}, title = {Locating unstable periodic orbits: {When} adaptation integrates into delayed feedback control}, volume = {82}, year = {2010}, doi = {10.1103/PhysRevE.82.046214}, } @Article{Moore90, author = {Moore, C.}, journal = {Phys. Rev. Lett.}, pages = {2354--2357}, title = {Unpredictability and undecidability in dynamical systems}, volume = {64}, year = {1990}, doi = {10.1103/physrevlett.64.2354}, } @Article{Moore91, author = {Moore, C.}, journal = {Nonlinearity}, pages = {199--230}, title = {Generalized shifts: unpredictability and undecidability in dynamical systems}, volume = {4}, year = {1991}, doi = {10.1088/0951-7715/4/2/002}, } @Article{DePSWP12, author = {De Paula, A. S. and Savi, M. A. and Wiercigroch, M.N and Pavlovskaia, E.}, journal = {Int. J. Bifur. Chaos}, pages = {1250111}, title = {Bifurcation control of a parametric pendulum}, volume = {22}, year = {2012}, doi = {10.1142/S0218127412501118}, } @Article{AllBar12, author = {A. Allahem and T. Bartsch}, journal = {J. Chem. Phys.}, pages = {214310}, title = {Chaotic dynamics in multidimensional transition states}, volume = {137}, year = {2012}, doi = {10.1063/1.4769197}, } @Article{BeCa80, author = {V. G. Benza and V. Callegaro}, journal = {J. Phys. A}, pages = {L841--L846}, title = {Phase transitions on strange sets: the {Ising} quasicrystal}, volume = {23}, year = {1990}, doi = {10.1088/0305-4470/23/16/012}, } @Article{KohTak07, author = {Koh, Y. W. and Takatsuka, K.}, journal = {Phys. Rev. E}, pages = {066205}, title = {Finding periodic orbits of higher-dimensional flows by including tangential components of trajectory motion}, volume = {76}, year = {2007}, doi = {10.1103/PhysRevE.76.066205}, } @Article{Saiki07, author = {Saiki, Y.}, journal = {Nonlin. Proc. Geophys.}, pages = {615--620}, title = {Numerical detection of unstable periodic orbits in continuous-time dynamical systems with chaotic behaviors}, volume = {14}, year = {2007}, doi = {10.5194/npg-14-615-2007}, } @Book{ParChu89, author = {Parker, T. S. and Chua, L. O.}, publisher = {Springer}, title = {{Practical Numerical Algorithms for Chaotic Systems}}, year = {1989}, address = {New York}, doi = {10.1007/978-1-4612-3486-9}, } @Article{YamSai97, author = {M. Yamada and Y. Saiki}, journal = {Nonlin. Proc. Geophys.}, pages = {631--640}, title = {Chaotic properties of a fully developed model turbulence}, volume = {14}, year = {2007}, doi = {10.5194/npg-14-631-2007}, } @Article{SaiYam09, author = {Saiki, Y. and Yamada, M.}, journal = {Phys. Rev. E}, pages = {015201}, title = {Time-averaged properties of unstable periodic orbits and chaotic orbits in ordinary differential equation systems}, volume = {79}, year = {2009}, doi = {10.1103/physreve.79.015201}, } @InCollection{SaiYam13, author = {Saiki, Y. and Yamada, M.}, booktitle = {{Emerging Topics on Differential Equations and Their Applications}}, publisher = {World Scientific}, title = {Time averaged properties along unstable periodic orbits of the {Kuramoto-Sivashinsky} equation}, year = {2013}, pages = {145--154}, doi = {10.1142/9789814449755_0012}, } @Misc{GrPo12, author = {{beim Graben}, P. and Potthast, R.}, title = {Implementing {Turing} machines in dynamic field architectures}, year = {2012}, url = {http://arXiv.org/abs/1204.5462}, } @Misc{Mainieri04, author = {R. Mainieri}, title = {Can averaged orbits be used to extract scaling functions?}, year = {1994}, url = {http://arXiv.org/abs/chao-dyn/9302004}, } @Article{Scarf67, author = {H. Scarf}, journal = {SIAM J. Appl. Math.}, title = {The approximation of fixed points of a continuous mapping}, volume = {15}, year = {1967}, doi = {10.1137/0115116}, } @Article{Brouwer1, author = {Brouwer, L. E. J.}, journal = {Math. Ann.}, title = {{\"Uber Abbildung von Mannigfaltigkeiten}}, year = {1911}, pages = {97--115}, volume = {71}, doi = {10.1007/BF01456931}, } @Article{PePaVr08, author = {Petalas, Y. G. and Parsopoulos, K. E. and Vrahatis, M. N.}, journal = {Nonlin. Phen. Compl. Syst.}, title = {Stochastic optimization for detecting periodic orbits of nonlinear mappings}, year = {2008}, pages = {285--291}, volume = {11}, } @Article{GGLTL09, author = {F. Gao and H. Gao and Zh. Li and H. Tong and J.-J. Lee}, journal = {Chaos Solit. Fract.}, pages = {2450--2463}, title = {Detecting unstable periodic orbits of nonlinear mappings by a novel quantum-behaved particle swarm optimization non-{Lyapunov} way}, volume = {42}, year = {2009}, doi = {10.1016/j.chaos.2009.03.119}, } @Article{Kazantsev01a, author = {Kazantsev, E.}, journal = {Chaos Solit. Fract.}, pages = {1989--2005}, title = {Sensitivity of attractor to external influences: {Approach} by unstable periodic orbits}, volume = {12}, year = {2001}, doi = {10.1016/S0960-0779(00)00154-5}, } @Article{Kazantsev01, author = {Kazantsev, E.}, journal = {Nonlin. Proc. Geophys.}, pages = {281--300}, title = {Sensitivity of the attractor of the barotropic ocean model to external influences: {Approach} by unstable periodic orbits}, volume = {8}, year = {2001}, doi = {10.5194/npg-8-281-2001}, } @Article{CSRBHK07, author = {Chian, A. C.-L. and Santana, W. M. and Rempel, E. L. and Borotto, F. A. and Hada, T. and Kamide, Y.}, journal = {Nonlin. Proc. Geophys.}, title = {Chaos in driven {Alfv\'en} systems: {Unstable} periodic orbits and chaotic saddles}, year = {2007}, pages = {17--29}, volume = {14}, doi = {10.5194/npg-14-17-2007}, } @Unpublished{Kazantsev98a, author = {Kazantsev, E.}, note = {Projet NUMATH, Rapport de recherche n. 3344}, title = {Unstable periodic orbits and attractor of the {Lorenz} model}, year = {1998}, institution = {INRIA Lorraine}, } @PhdThesis{SmithThesis12, author = {Smith, S. A.}, school = {Mathematics Dept., Tufts University}, title = {{Point Vortices: Finding Periodic Orbits and their Topological Classification}}, year = {2012}, address = {Medford, Mass}, url = {http://gradworks.umi.com/3541851.pdf}, } @Article{BerTab76, author = {M. V. Berry and M. Tabor}, journal = {Proc. Roy. Soc. Ser A}, pages = {101--123}, title = {Closed orbits and the regular bound spectrum}, volume = {349}, year = {1976}, doi = {10.1098/rspa.1976.0062}, } @Article{Strut68a, author = {Strutinsky, V. M.}, journal = {Nucl. Phys. A}, pages = {420--442}, title = {Shell effects in nuclear masses and deformation energies}, volume = {95}, year = {1967}, doi = {10.1016/0375-9474(67)90510-6}, } @Article{Strut68b, author = {Strutinsky, V. M.}, journal = {Nucl. Phys. A}, title = {``{Shells}'' in deformed nuclei}, year = {1968}, pages = {1--33}, volume = {122}, doi = {10.1016/0375-9474(68)90699-4}, } @Article{CdV73, author = {Colin de Verdi\`ere, Y.}, journal = {Compositio. Math.}, title = {Spectre du {Laplacien} et longeurs des g\`eod\`esiques p\`eriodiques, {II.}}, year = {1973}, pages = {159--184}, volume = {27}, } @Article{BiKoTi13, author = {C. Bick and C. Kolodziejski and M. Timme}, journal = {New J. Phys.}, pages = {063038}, title = {Stalling chaos control accelerates convergence}, volume = {15}, year = {2013}, doi = {10.1088/1367-2630/15/6/063038}, } @Article{Vergini00, author = {E. G. Vergini}, journal = {J. Phys. A}, pages = {4709--4716}, title = {Semiclassical theory of short periodic orbits in quantum chaos}, volume = {33}, year = {2000}, doi = {10.1088/0305-4470/33/25/311}, } @Article{Vergini13, author = {Vergini, E. G.}, journal = {Europhys. Lett.}, pages = {20003}, title = {Semiclassical propagation up to the {Heisenberg} time}, volume = {103}, year = {2013}, doi = {10.1209/0295-5075/103/20003}, } @Article{Vergini12, author = {Vergini, E. G.}, journal = {Phys. Rev. Lett.}, pages = {264101}, title = {Semiclassical approach to long time propagation in quantum chaos: predicting scars}, volume = {108}, year = {2012}, doi = {10.1103/PhysRevLett.108.264101}, } @Article{VeCa00, author = {Vergini, E. G. and Carlo, G. G.}, journal = {J. Phys. A}, pages = {4717--4724}, title = {Semiclassical quantization with short periodic orbits}, volume = {33}, year = {2000}, doi = {10.1088/0305-4470/33/25/312}, } @Article{VeCa01, author = {Vergini, E. G. and Carlo, G. G.}, journal = {J. Phys. A}, pages = {4525--4552}, title = {Semiclassical construction of resonances with hyperbolic structure: the scar function}, volume = {34}, year = {2001}, doi = {10.1088/0305-4470/34/21/308}, } @Article{VSRBB10, author = {Vergini, E. G. and E. L. Sibert, I. I. I. and Revuelta, F. and Benito, R. M. and Borondo, F.}, journal = {Europhys. Lett.}, title = {Diagonal matrix elements in a scar function basis set}, year = {2010}, pages = {40013}, volume = {89}, doi = {10.1209/0295-5075/89/40013}, } @Article{BarRod14, author = {R. Barrio and M. Rodr{\'i}guez}, journal = {Commun. Nonlinear Sci. Numer. Simul.}, pages = {2660--2675}, title = {Systematic computer assisted proofs of periodic orbits of {Hamiltonian systems}}, volume = {19}, year = {2014}, doi = {10.1016/j.cnsns.2013.12.025}, } @Article{BaBaBo12, author = {Bailey, D. H. and Barrio, R. and Borwein, J. M.}, journal = {Appl. Math. Computation}, title = {High-precision computation: {Mathematical} physics and dynamics}, year = {2012}, pages = {10106--10121}, volume = {218}, doi = {10.1016/j.amc.2012.03.087}, } @Article{ABBR12, author = {Abad, A. and Barrio, R. and Blesa, F. and Rodr{\'i}guez, M.}, journal = {ACM Trans. Math. Softw.}, pages = {5:1--5:28}, title = {Algorithm 924: {TIDES}, a {Taylor} series integrator for differential equations}, volume = {39}, year = {2012}, doi = {10.1145/2382585.2382590}, } @Article{DRSB12, author = {Dena, {\'A}. and Rodr{\'i}guez, M. and Serrano, S. and Barrio, R.}, journal = {Abst. Appl. Analysis}, pages = {1--12}, title = {High-precision continuation of periodic orbits}, volume = {2012}, year = {2012}, doi = {10.1155/2012/716024}, } @Article{Cherry28, author = {Cherry, T. M.}, journal = {Proc. Roy. Soc. Lond. Ser A}, pages = {137--221}, title = {On periodic solutions of {Hamiltonian} systems of differential equations}, volume = {227}, year = {1928}, } @Article{Morena2014, author = {Morena, M.A. and Short, K.M.}, journal = {Int. J. Bifur. Chaos}, pages = {1450077}, title = {On the potential for entangled states between chaotic systems}, volume = {24}, year = {2014}, doi = {10.1142/S0218127414500771}, } @Article{Pyragas92, author = {K. Pyragas}, journal = {Phys. Lett. A}, pages = {421--428}, title = {Continuous control of chaos by self-controlling feedback}, volume = {170}, year = {1992}, doi = {10.1016/0375-9601(92)90745-8}, } @Misc{GoZa10, author = {Goldobin, D. S. and Zaks, M. A.}, title = {Noise reduces disorder in chaotic dynamics}, year = {2010}, url = {http://arXiv.org/abs/1008.0073}, } @Article{Rugh19a, author = {Rugh, H. H.}, journal = {{EMS} Newsletter}, pages = {21--24}, title = {An interview with {David Ruelle}}, volume = {2020-3}, year = {2020}, doi = {10.4171/news/115/6}, } @Article{Rugh19, author = {Rugh, H. H.}, journal = {Gaz. Math.}, pages = {55--59}, title = {Un interview de {David Ruelle}}, volume = {161}, year = {2019}, url = {https://smf.emath.fr/download/pdf/120669}, } @Article{SprHoo17, author = {Sprott, J. C. and Hoover, W. G.}, journal = {Int. J. Bifurcation Chaos}, pages = {1730037}, title = {Harmonic oscillators with nonlinear damping}, volume = {27}, year = {2017}, doi = {10.1142/s0218127417300373}, } @Book{KrReBe10, author = {Krapivsky, P. L. and Redner, S. and Ben-Naim, E.}, publisher = {Cambridge Univ. Press}, title = {{A Kinetic View of Statistical Physics}}, year = {2009}, address = {Cambridge, UK}, doi = {10.1017/cbo9780511780516}, } @Book{Roman12, author = {Roman, S.}, publisher = {Birkh\"auser}, title = {{Fundamentals of Group Theory: An Advanced Approach}}, year = {2012}, address = {Boston}, doi = {10.1007/978-0-8176-8301-6}, } @Book{Koks06, author = {Koks, D.}, publisher = {Springer}, title = {{Explorations in Mathematical Physics: The Concepts Behind an Elegant Language}}, year = {2006}, address = {New York}, doi = {10.1007/978-0-387-32793-8}, } @Book{Jee11, author = {Jeevanjee, N.}, publisher = {Birkh\"auser}, title = {{An Introduction to Tensors and Group Theory for Physicists}}, year = {2011}, address = {Boston}, doi = {10.1007/978-0-8176-4715-5}, } @PhdThesis{zimmermann-global, author = {Zimmermann, M. G.}, school = {Upsala Univ.}, title = {{Global Bifurcations and Chaotic Dynamics in Physical Applications}}, year = {1997}, doi = {10.1.1.46.4304}, isbn = {9155439721}, publisher = {Acta Univ. Upsaliensis}, url = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.46.4304&rep=rep1&type=pdf}, } @Misc{WilZgl17, author = {Wilczak, D. and Zgliczynski, P.}, title = {Symbolic dynamics for {Kuramoto-Sivashinsky PDE} on the line--a computer--assisted proof}, year = {2017}, eprint = {1710.00329}, eprinttype = {arxiv}, } @Article{Wilkinson16, author = {Wilkinson, A.}, journal = {Bull. Amer. Math. Soc.}, pages = {79--105}, title = {What are {Lyapunov} exponents, and why are they interesting?}, volume = {54}, year = {2016}, doi = {10.1090/bull/1552}, } @Article{CoLaTh20, author = {Constantine, D. and Lafont, J.-F. and Thompson, D.}, journal = {Groups, Geometry, and Dynamics}, pages = {297--336}, title = {The weak specification property for geodesic flows on {CAT}(-1) spaces}, volume = {14}, year = {2020}, doi = {10.4171/ggd/545}, } @Article{BowWal72, author = {Bowen, R. and Walters, P.}, journal = {J. Differential Equations}, pages = {180--193}, title = {Expansive one-parameter flows}, volume = {12}, year = {1972}, doi = {10.1016/0022-0396(72)90013-7}, } @Misc{DFSU20, author = {Das, T. and Fishman, L. and Simmons, D. and Urba{\'n}ski, M.}, title = {Hausdorff dimensions of perturbations of a conformal iterated function system via thermodynamic formalism}, year = {2020}, eprint = {2007.10554}, eprinttype = {arxiv}, } @Article{motter09-1, Title = {Relativistic invariance of {Lyapunov} exponents in bounded and unbounded systems}, Author = {Motter, A. E. and Saa, A.}, Journal = {Phys. Rev. Lett.}, Year = {2009}, Pages = {184101}, Volume = {102}, DOI = {10.1103/PhysRevLett.102.184101} } @Article{Koenig97, Title = {Linearization of vector fields on the orbit space of the action of a compact {Lie} group}, Author = {M. K{\oe}nig}, Journal = {Math. Proc. Cambridge Philos. Soc.}, Year = {1997}, Pages = {401--424}, Volume = {121}, DOI = {10.1017/S0305004196001314} } @Article{Kowa97, author = {Kowalski, K.}, title = {Nonlinear dynamical systems and classical orthogonal polynomials}, journal = {J. Math. Phys.}, year = {1997}, volume = {38}, pages = {2483--2505}, doi = {10.1063/1.531990}, } @Article{Flannery11, Title = {The elusive {d'Alembert-Lagrange} dynamics of nonholonomic systems}, Author = {M. R. Flannery}, Journal = {Amer. J. Phys.}, Year = {2011}, Pages = {932--944}, Volume = {79}, DOI = {10.1119/1.3563538} } @Article{GoPa11, Title = {Numerical simulation of asymptotic states of the damped {Kuramoto-Sivashinsky} equation}, Author = {Gomez, H. and Paris, J.}, Journal = {Phys. Rev. E}, Year = {2011}, Pages = {046702}, Volume = {83}, DOI = {10.1103/PhysRevE.83.046702} } @Article{WanZhoE10, author = {Wan, X. and Zhou, X. and E, W.}, title = {Study of the noise-induced transition and the exploration of the phase space for the {Kuramoto-Sivashinsky} equation using the minimum action method}, journal = {Nonlinearity}, year = {2010}, volume = {23}, pages = {475--493}, doi = {10.1088/0951-7715/23/3/002}, } @Article{FogRen09, Title = {Minimum action method for the {Kardar-Parisi-Zhang} equation}, Author = {Fogedby, H. C. and Ren, W.}, Journal = {Phys. Rev. E}, Year = {2009}, Pages = {041116}, Volume = {80}, DOI = {10.1103/PhysRevE.80.041116} } @Article{Wan11, author = {X. Wan}, journal = {J. Comp. Phys.}, title = {An adaptive high-order minimum action method}, year = {2011}, doi = {10.1016/j.jcp.2011.08.006}, } @Article{Roupas11, author = {Z. Roupas}, title = {Phase space geometry and chaotic attractors in dissipative {Nambu} mechanics}, journal = {J. Phys. A}, year = {2012}, volume = {45}, pages = {195101}, doi = {10.1088/1751-8113/45/19/195101}, } @Article{Rumb00, author = {M. Rumberger}, title = {{Lyapunov} exponents on the orbit space}, journal = {Discrete Continuous Dyn. Syst. Ser. A}, year = {2000}, volume = {7}, pages = {91--113}, doi = {10.3934/dcds.2001.7.91}, } @Article{Rumb01, Title = {On eigenvalues on the orbit space}, Author = {M. Rumberger}, Journal = {J. Pure Appl. Algebra}, Year = {2001}, Pages = {89--99}, Volume = {158}, DOI = {10.1016/S0022-4049(00)00023-2} } @Article{Coma06, Title = {Forced symmetry breaking from {SO(3)} to {SO(2)} for rotating waves on a sphere}, Author = {A. N. Comanici}, Journal = {Nonlinearity}, Year = {2006}, Pages = {999--1019}, Volume = {19}, DOI = {10.1088/0951-7715/19/5/001} } @Article{LaSa97, Title = {Bifurcation analysis for spherically symmetric systems using invariant theory}, Author = {R. Lauterbach and J. A. Sanders}, Journal = {J. Dynam. Diff. Eq.}, Year = {1997}, Pages = {535--560}, Volume = {9}, DOI = {10.1007/BF02219397} } @Article{OrRa04, Title = {Symmetry reduction in symplectic and {Poisson} geometry}, Author = {J.-P. Ortega and T. S. Ratiu}, Journal = {Lett. Math. Phys.}, Year = {2004}, Pages = {11--60}, Volume = {69}, DOI = {10.1007/s11005-004-0898-x} } @Article{Schwarz75, Title = {Smooth functions invariant under the action of a compact {Lie} group}, Author = {G. Schwarz}, Journal = {Topology}, Year = {1975}, Pages = {63--68}, Volume = {14}, DOI = {10.1016/0040-9383(75)90036-1} } @Article{Bredon61, Title = {On the structure of orbit spaces of generalized manifolds}, Author = {G. E. Bredon}, Journal = {Trans. Amer. Math. Soc.}, Year = {1961}, Pages = {162--162}, Volume = {100}, DOI = {10.1090/S0002-9947-1961-0126503-5} } @Article{NajHav95, Title = {Derivatives of the matrix exponential and their computation}, Author = {I. Najfeld and T. F. Havel}, Journal = {Adv. Appl. Math.}, Year = {1995}, Pages = {321--375}, Volume = {16}, DOI = {10.1006/aama.1995.1017} } @Article{OzHaRoBu13, Title = {Pilot-wave dynamics in a rotating frame: on the emergence of orbital quantization}, Author = {Oza, A. U. and Harris, D. M. and Rosales, R. R. and Bush, J. W. M.}, Journal = {J. Fluid Mech.}, Year = {2014}, Pages = {404--429}, Volume = {744}, DOI = {10.1017/jfm.2014.50} } @Article{OzRoBu13, Title = {A trajectory equation for walking droplets: hydrodynamic pilot-wave theory}, Author = {Oza, A. U. and Rosales, R. R. and Bush, J. W. M.}, Journal = {J. Fluid Mech.}, Year = {2013}, Pages = {552--570}, Volume = {737}, DOI = {10.1017/jfm.2013.581} } @Article{OhlRav13, Title = {Nonlinear reduced basis approximation of parameterized evolution equations via the method of freezing}, Author = {M. Ohlberger and S. Rave}, Journal = {Comptes Rendus Mathematique}, Year = {2013}, Pages = {901--906}, Volume = {351}, DOI = {10.1016/j.crma.2013.10.028} } @Article{Sylvester1883, author = {Sylvester, J. J.}, journal = {Philos. Mag.}, pages = {267--269}, title = {{XXXIX}. {On} the equation to the secular inequalities in the planetary theory}, volume = {16}, year = {1883}, doi = {10.1080/14786448308627430}, } @Article{BoCoWa19, author = {Boghosian, B. M. and Coveney, P. V. and Wang, H.}, journal = {Adv. Theory Simulations}, pages = {1900125}, title = {A new pathology in the simulation of chaotic dynamical systems on digital computers}, volume = {2}, year = {2019}, doi = {10.1002/adts.201900125}, } @Article{Axler95, author = {Axler, S.}, journal = {Amer. Math. Monthly}, pages = {139--154}, title = {Down with determinants!}, volume = {102}, year = {1995}, doi = {10.2307/2975348}, } @Book{BruKut19, author = {Brunton, S. L. and Kutz, J. N.}, publisher = {Cambridge Univ. Press}, title = {{Data-driven Science and Engineering: Machine Learning, Dynamical Systems, and Control}}, year = {2019}, address = {Cambridge UK}, doi = {10.1017/9781108380690}, } @InCollection{CliDhi06, author = {Cline, A. K. and Dhillon, I. S.}, booktitle = {{Handbook of Linear Algebra}}, publisher = {CRC Press}, title = {Computation of the singular value decomposition}, year = {2006}, pages = {45-1--45-13}, doi = {10.1201/9781420010572-45}, } @Book{GoetheIstuZim1806, author = {von Goethe, J. W.}, publisher = {Yale Univ. Press}, title = {{Faust I, Studierzimmer 2.}}, year = {1806}, isbn = {9780300189698}, note = {M. Greenberg, transl.}, } @Article{JenPol18, author = {Jenkinson, O. and Pollicott, M.}, journal = {Adv. Math.}, title = {Rigorous effective bounds on the {Hausdorff} dimension of continued fraction {Cantor} sets: {A} hundred decimal digits for the dimension of {E2}}, year = {2018}, pages = {87--115}, volume = {325}, doi = {10.1016/j.aim.2017.11.028}, } @Article{BanJen08, author = {Bandtlow, O. F. and Jenkinson, O.}, journal = {Ergod. Theor. Dynam. Syst.}, title = {On the {Ruelle} eigenvalue sequence}, year = {2008}, pages = {1701}, volume = {28}, doi = {10.1017/s0143385708000059}, } @Article{GiLiPo13, author = {Giulietti, P. and Liverani, C. and Pollicott, M.}, journal = {Ann. Math.}, title = {Anosov flows and dynamical zeta functions}, year = {2013}, pages = {687--773}, volume = {178}, doi = {10.4007/annals.2013.178.2.6}, } @InCollection{Bedford91, author = {Bedford, T.}, booktitle = {{Fractal Geometry and Analysis}}, publisher = {Springer}, title = {Applications of dynamical systems theory to fractals: a study of cookie-cutter {Cantor} sets}, year = {1991}, pages = {1--44}, doi = {10.1007/978-94-015-7931-5_1}, } @Book{Falconer03, author = {Falconer, K. J.}, publisher = {Wiley}, title = {{Fractal geometry : mathematical foundations and applications}}, year = {2003}, address = {Chichester}, doi = {10.1002/0470013850}, } @Book{MauUrb03, author = {Mauldin, R. D. and Urba{\'n}ski, M.}, publisher = {Cambridge Univ. Press}, title = {{Graph directed Markov systems : Geometry and dynamics of limit sets}}, year = {2003}, address = {Cambridge UK}, doi = {10.1017/cbo9780511543050}, } @Article{BGNN16, author = {Bahsoun, W. and Galatolo, S. and Nisoli, I. and Niu, X.}, journal = {J. Stat. Phys.}, title = {Rigorous approximation of diffusion coefficients for expanding maps}, year = {2016}, pages = {1486--1503}, volume = {163}, doi = {10.1007/s10955-016-1523-y}, } @Article{Lanford98, author = {Lanford, O. E.}, journal = {Exp. Math.}, title = {Informal remarks on the orbit structure of discrete approximations to chaotic maps}, year = {1998}, pages = {317--324}, volume = {7}, doi = {10.1080/10586458.1998.10504377}, } @Article{SelWei93, author = {Seligman, T. H. and Weidenmuller, H. A.}, journal = {J. Phys. A}, title = {Semi-classical periodic-orbit theory for chaotic {Hamiltonians} with discrete symmetries}, year = {1994}, pages = {7915--7923}, volume = {27}, doi = {10.1088/0305-4470/27/23/034}, } @Article{Wormell19, author = {Wormell, C.}, journal = {Numerische Mathematik}, title = {Spectral {Galerkin} methods for transfer operators in uniformly expanding dynamics}, year = {2019}, pages = {421--463}, volume = {142}, doi = {10.1007/s00211-019-01031-z}, } @Article{BeOtRo16, author = {Beyn, W.-J. and Otten, D. and Rottmann-Matthes, J.}, journal = {{SIAM} J. Numer. Anal.}, title = {Computation and stability of traveling waves in second order evolution equations}, year = {2016}, pages = {1786--1817}, volume = {56}, doi = {10.1137/16m108286x}, } @Article{JePoVy17, author = {Jenkinson, O. and Pollicott, M. and Vytnova, P.}, journal = {J. Stat. Phys.}, title = {Rigorous computation of diffusion coefficients for expanding maps}, year = {2017}, pages = {221--253}, volume = {170}, doi = {10.1007/s10955-017-1930-8}, } @Article{Penrose55, author = {Penrose, R.}, journal = {Math. Proc. Cambridge Philos. Soc.}, title = {A generalized inverse for matrices}, year = {1955}, pages = {406--413}, volume = {51}, doi = {10.1017/s0305004100030401}, } @Article{Penrose65, author = {Penrose, R.}, journal = {Phys. Rev. Lett.}, title = {Gravitational collapse and space-time singularities}, year = {1965}, pages = {57--59}, volume = {14}, doi = {10.1103/physrevlett.14.57}, } @Article{PenroseMacCullen, author = {Penrose, R. and MacCallum, M. A. H.}, title = {Twistor theory: {An} approach to the quantisation of fields and space-time}, journal = {Phys. Rep.}, year = {1973}, volume = {6}, pages = {241--315}, doi = {10.1016/0370-1573(73)90008-2}, } @Article{Penrose67, author = {R. Penrose}, journal = {J. Math. Phys.}, title = {Twistor algebra}, year = {1967}, pages = {345--366}, volume = {8}, doi = {10.1063/1.1705200}, } @Article{Penrose69, author = {Penrose, R.}, journal = {Riv. Nuovo Cimento}, title = {Gravitational collapse: {The} role of general relativity}, year = {1969}, pages = {257}, volume = {Num. Spez. I}, doi = {10.1023/a:1016578408204}, } @Article{Penrose74, author = {Penrose, R.}, journal = {Bull. Inst. Math. Appl.}, title = {The role of aesthetics in pure and applied mathematical research}, year = {1974}, pages = {266--271}, volume = {10}, } @Book{Penrose89, author = {Penrose, R.}, publisher = {Oxford Univ. Press}, title = {{The Emperor's New Mind - Concerning Computers, Minds, and The Laws of Physics}}, year = {1989}, address = {Oxford UK}, doi = {10.1093/oso/9780198519737.001.0001}, } @Book{Penrose96, author = {Penrose, R.}, publisher = {Oxford Univ. Press}, title = {{Shadows of the Mind} - {A Search for the Missing Science of Consciousness}}, year = {1996}, address = {Oxford UK}, isbn = {0195106466}, } @Book{Penrose11, author = {Penrose, Roger}, publisher = {Vintage}, title = {{Cycles of Time} - {An Extraordinary New View of the Universe}}, year = {2011}, address = {New York}, isbn = {9780307278463}, } @Book{Penrose16, author = {Penrose, R.}, publisher = {Princeton Univ. Press}, title = {{Fashion, Faith, and Fantasy in the New Physics of the Universe}}, year = {2016}, doi = {10.1515/9781400880287}, } @Article{TaLuDi17, author = {Tantet, A. and Lucarini, V. and Dijkstra, H. A.}, journal = {J. Stat. Phys.}, title = {Resonances in a chaotic attractor crisis of the {Lorenz} flow}, year = {2017}, pages = {584--616}, volume = {170}, doi = {10.1007/s10955-017-1938-0}, } @TechReport{Barvinok04, author = {Barvinok, A.}, title = {{Lattice Points, Polyhedra, and Complexity}}, institution = {Univ. of Michigen}, year = {2004}, address = {Ann Arbor MI}, url = {http://www.math.lsa.umich.edu/~barvinok/lectures.pdf}, } @Article{SlBaJu16, author = {Slipantschuk, J. and {Bandtlow}, O. F. and {Just}, W.}, title = {Complete spectral data for analytic {Anosov} maps of the torus}, journal = {Nonlinearity}, year = {2017}, volume = {30}, pages = {2667}, doi = {10.1088/1361-6544/aa700f}, } @TechReport{Crutchfield18, author = {J. Crutchfield}, title = {{Roadmap for Natural Computation and Self-Organization}}, institution = {U. California, Davis}, year = {2017}, note = {Physics 256A course}, url = {http://csc.ucdavis.edu/~chaos/courses/ncaso/Lectures/}, } @Article{Behrends98, Title = {The ghosts of the cat}, Author = {Behrends, E.}, Journal = {Ergod. Theor. Dynam. Syst.}, Year = {1998}, Pages = {321--330}, Volume = {18}, URL = {http://journals.cambridge.org/article_S0143385798100378} } @Article{BehFie98, Title = {Periods of discretized linear {Anosov} maps}, Author = {Behrends, E. and Fielder, B.}, Journal = {Ergod. Theor. Dynam. Syst.}, Year = {1998}, Pages = {331--341}, Volume = {18}, URL = {http://journals.cambridge.org/article_S0143385798100366} } @Article{BarShc06, Title = {Periodic orbits of the ensemble of {Sinai-Arnold} cat maps and pseudorandom number generation}, Author = {Barash, L. and Shchur, L. N.}, Journal = {Phys. Rev. E}, Year = {2006}, Pages = {036701}, Volume = {73}, DOI = {10.1103/PhysRevE.73.036701} } @Article{Keating91a, Title = {Asymptotic properties of the periodic orbits of the cat maps}, Author = {J. P. Keating}, Journal = {Nonlinearity}, Year = {1991}, Pages = {277}, Volume = {4}, DOI = {10.1088/0951-7715/4/2/005} } @Article{Keating91, Title = {The cat maps: quantum mechanics and classical motion}, Author = {J. P. Keating}, Journal = {Nonlinearity}, Year = {1991}, Pages = {309--341}, Volume = {4}, DOI = {10.1088/0951-7715/4/2/006} } @Article{DysFal92, Title = {Period of a discrete cat mapping}, Author = {F. J. Dyson and H. Falk}, Journal = {Amer. Math. Monthly}, Year = {1992}, Pages = {603--614}, Volume = {99}, DOI = {10.2307/2324989} } @Article{JinZwo14, author = {Jin, L. and Zworski, M.}, journal = {Ann. Inst. H. Poincar{\'e}}, title = {A local trace formula for {Anosov} flows}, year = {2016}, pages = {1--35}, volume = {18}, doi = {10.1007/s00023-016-0504-7}, } @Article{BoaKea95, Title = {Semiclassical asymptotics of perturbed cat maps}, Author = {Boasman, P. A. and Keating, J. P.}, Journal = {Proc. Roy. Soc. Ser A}, Year = {1995}, Pages = {629--653}, Volume = {449}, DOI = {10.1098/rspa.1995.0063} } @Article{Rivas13, author = {A. M. F. Rivas}, title = {Semiclassical matrix elements for a chaotic propagator in the scar function basis}, journal = {J. Phys. A}, year = {2013}, volume = {46}, pages = {145101}, doi = {10.1088/1751-8113/46/14/145101}, } @Book{AdWei70, Title = {Similarity of automorphisms of the torus}, Author = {Adler, R. L. and Weiss, B.}, Publisher = {Amer. Math. Soc.}, Year = {1970}, Address = {Providence RI}, DOI = {10.1090/memo/0098}, ISBN = {978-0-8218-1298-3}, Series = {Memoirs Amer. Math. Soc.}, Volume = {98} } @Article{SieWoj11, author = {A. Siemaszko and M. P. Wojtkowski}, title = {Counting {Berg} partitions}, journal = {Nonlinearity}, year = {2011}, volume = {24}, pages = {2383--2403}, doi = {10.1088/0951-7715/24/9/001}, } @Book{StOtWt06, author = {Sturman, R. and Ottino, J. M. and Wiggins, S.}, publisher = {Cambridge Univ. Press}, title = {{The Mathematical Foundations of Mixing}}, year = {2006}, doi = {10.1017/cbo9780511618116}, } @Article{IvIzHu02, author = {Ivashkevich, E. V. and Izmailian, N. Sh. and Hu, C.-K.}, title = {Kronecker's double series and exact asymptotic expansions for free models of statistical mechanics on torus}, journal = {J. Phys. A}, year = {2002}, volume = {35}, pages = {5543--5561}, doi = {10.1088/0305-4470/35/27/302}, } @Book{Elaydi99, author = {Elaydi, S. N.}, publisher = {Chapman and Hall}, title = {{Discrete Chaos}}, year = {2007}, isbn = {9781420011043}, doi = {10.1201/9781420011043}, } @Book{Hadamard1898, author = {Hadamard, J. S.}, publisher = {Impr. Gauthier-Villars}, title = {{Sur le Billard Non Euclidien}}, year = {1898}, } @InCollection{Sinai59, author = {Sinai, Ya. G.}, booktitle = {{Selecta I}}, publisher = {Springer}, title = {On the notion of entropy of a dynamical system}, year = {1959}, address = {New York}, pages = {768--771}, volume = {124}, doi = {10.1007/978-0-387-87870-6_1}, journal = {Dokl. Akad. Nauk. SSSR}, } @Article{Kolmogorov58, author = {A. N. Kolmogorov}, journal = {Dokl. Akad. Nauk SSSR}, title = {A new metric invariant of transient dynamical systems and automorphisms in {Lebesgue} spaces}, year = {1958}, pages = {861--864}, volume = {119}, doi = {10.1007/978-94-017-2973-4_5}, } @Article{kolm91, author = {A. N. Kolmogorov}, journal = {Soviet Phys. Uspekhi}, title = {The local structure of turbulence in incompressible viscous fluid for very large {Reynolds} numbers}, year = {1968}, pages = {734--746}, volume = {10}, doi = {10.1070/pu1968v010n06abeh003710}, } @Article{Kolmogorov1968, author = {A. N. Kolmogorov}, journal = {Soviet Phys. Uspekhi}, title = {The local structure of turbulence in incompressible viscous fluid for very large {Reynolds} numbers}, year = {1968}, pages = {734--746}, volume = {10}, doi = {10.1070/pu1968v010n06abeh003710}, } @Article{Kolmogorov59, author = {Kolmogorov, A. N.}, journal = {Dokl. Akad. Nauk SSSR}, title = {Entropy per unit time as a metric invariant of automorphisms}, year = {1959}, pages = {754--755}, volume = {124}, url = {https://nikolaivivanov.files.wordpress.com/2015/05/definitionentropy2014-20151.pdf}, } @Article{Rokhlin59, author = {Rokhlin, V. A.}, journal = {Dokl. Akad. Nauk SSSR}, title = {Entropy of metric automorphism}, year = {1959}, pages = {980--983}, volume = {124}, } @Article{AdlPal65, author = {Adler, R. L. and Palais, R.}, journal = {Proc. Amer. Math. Soc.}, title = {Homeomorphic conjugacy of automorphisms on the torus}, year = {1965}, pages = {1222--1222}, volume = {16}, doi = {10.1090/s0002-9939-1965-0193181-8}, } @Article{Sinai1968, author = {Sinai, Ya. G.}, journal = {Funct. Anal. Appl.}, title = {Markov partitions and {C}-diffeomorphisms}, year = {1968}, number = {1}, pages = {61--82}, volume = {2}, doi = {10.1007/bf01075361}, publisher = {Springer Science and Business Media {LLC}}, } @Article{Gutzwiller98, author = {Gutzwiller, M. C.}, journal = {Amer. J. Phys.}, title = {Resource letter {ICQM}-1: the interplay between classical and quantum mechanics}, year = {1998}, pages = {304--324}, volume = {66}, doi = {10.1119/1.19065}, } @Book{FetWal03, title = {{Theoretical Mechanics of Particles and Continua}}, publisher = {Dover}, year = {2003}, author = {Fetter, A. L. and Walecka, J. D.}, isbn = {9780486432618}, address = {New York}, } @Article{BunSin88, Title = {Spacetime chaos in coupled map lattices}, Author = {L. A. Bunimovich and Ya. G. Sinai}, Journal = {Nonlinearity}, Year = {1988}, Pages = {491}, Volume = {1}, DOI = {10.1088/0951-7715/1/4/001} } @Book{Sommerfeld1919, author = {Sommerfeld, A.}, publisher = {Deutsch}, title = {{Atombau und Spektrallinien}}, year = {1919}, address = {Thun, Frankfurt/M}, isbn = {9783871444845}, } @Book{Holmes13, author = {Holmes, M. H.}, publisher = {Springer}, title = {{Introduction to Perturbation Methods}}, year = {2013}, address = {New York}, doi = {10.1007/978-1-4614-5477-9}, } @Article{Corson48, author = {Corson, E. M.}, journal = {Phys. Rev.}, title = {Note on the {Dirac} character operators}, year = {1948}, pages = {57--60}, volume = {73}, doi = {10.1103/physrev.73.57}, } @Book{Dirac30, author = {Dirac, P. A. M.}, publisher = {Oxford Univ. Press}, title = {{The Principles of Quantum Mechanics}}, year = {1930}, url = {https://archive.org/details/dli.ernet.212159/mode/2up}, } @Book{Cini07, author = {Cini, M.}, publisher = {Springer}, title = {{Topics and Methods in Condensed Matter Theory - From Basic Quantum Mechanics to the Frontiers of Research}}, year = {2007}, address = {Berlin}, doi = {10.1007/978-3-540-70727-1}, } @Book{Jacobs05, author = {Jacobs, P.}, publisher = {Cambridge Univ. Press}, title = {{Group Theory with Applications in Chemical Physics}}, year = {2005}, doi = {10.1017/CBO9780511535390}, } @Book{ElBWoo08, author = {El-Batanouny, M. and Wooten, F.}, publisher = {Cambridge Univ. Press}, title = {{Symmetry and Condensed Matter Physics: A Computational Approach}}, year = {2008}, address = {Cambridge UK}, doi = {10.1017/CBO9780511755736​}, } @Article{AreLis82, author = {Arecchi, F. T. and Lisi, F.}, journal = {Phys. Rev. Lett.}, title = {Hopping mechanism generating {1/f} noise in nonlinear systems}, year = {1982}, pages = {94--98}, volume = {49}, doi = {10.1103/physrevlett.49.94}, } @Article{MauLib79, author = {J. Maurer and A. Libchaber}, title = {{Rayleigh-B{\'{e}}nard} experiment in liquid helium; frequency locking and the onset of turbulence}, journal = {J. Physique Lett.}, year = {1979}, volume = {40}, pages = {419--423}, doi = {10.1051/jphyslet:019790040016041900}, } @Article{Nepomnyashchii75, author = {Nepomnyashchii, A. A.}, journal = {Fluid Dynamics}, title = {Stability of wavy conditions in a film flowing down an inclined plane}, year = {1975}, pages = {354--359}, volume = {9}, doi = {10.1007/bf01025515}, } @InCollection{Homsy74, author = {Homsy, G. M.}, booktitle = {{Nonlinear Wave Motion}}, publisher = {Amer. Math. Soc.}, title = {Model equations for wavy viscous film flow}, year = {1974}, address = {Providence, R.I}, editor = {Newell, A. C.}, isbn = {9780821811153}, pages = {191--194}, series = {{Lectures in Applied Mathematics}}, volume = {15}, } @Misc{ChOlSm21, author = {Cheskidov, A. and Olson, E. and Smith, B.}, note = {Pure and Applied Functional Analysis, to appear}, title = {The computation of wandering points on the globalattractor by means of symmetry-breaking perturbations}, year = {2021}, } @Book{GriSch11, author = {Griffiths, G. and Schiesser, W.}, publisher = {Academic}, title = {{Traveling Wave Analysis of Partial Differential Equations : Numerical and Analytical Methods with Matlab and Maple}}, year = {2011}, address = {Amsterdam}, isbn = {9780123846525}, } @Article{ATMOTOA11, author = {Aihara, I. and Takeda, R. and Mizumoto, T. and Otsuka, T. and Takahashi, T. and Okuno, H. G. and Aihara, K.}, journal = {Phys. Rev. E}, title = {Complex and transitive synchronization in a frustrated system of calling frogs}, year = {2011}, pages = {031913}, volume = {83}, doi = {10.1103/physreve.83.031913}, } @Article{Southall26, author = {Southall, J. P.}, journal = {Optometry and Vision Science}, title = {Helmholtz' physiological optics}, year = {1926}, pages = {181}, volume = {3}, doi = {10.1097/00006324-192606000-00007}, } @Book{Helmholtz1896, author = {Helmholtz, H. v. and K{\"o}nig, A.}, publisher = {L. Voss}, title = {{Handbuch der Physiologischen Optik}}, year = {1896}, address = {Hamburg}, url = {http://hdl.handle.net/2027/uc1.$b397407}, } @Book{Turner94, author = {Turner, R. S.}, publisher = {Princeton Univ. Press}, title = {{In the Eye's Mind}}, year = {1994}, doi = {10.1515/9781400863815.10}, pages = {10--32}, } @InCollection{Berry17Gutzw, author = {Berry, M.}, booktitle = {{A Half-Century of Physical Asymptotics and Other Diversions} - {Selected Works by Michael Berry}}, publisher = {World Scientific}, title = {{Martin Gutzwiller} and his periodic orbits}, year = {2017}, pages = {576--579}, doi = {10.1142/9789813221215_0053}, } @Book{DumFoot03, author = {Dummit, D. S. and Foote, R. M.}, publisher = {Wiley}, title = {{Abstract Algebra}}, year = {2003}, isbn = {9780471433347}, } @Article{Mita21, author = {Mita, K.}, journal = {Amer. J. Phys.}, title = {Schr{\"o}dinger's equation as a diffusion equation}, year = {2021}, pages = {500--510}, volume = {89}, doi = {10.1119/10.0002765}, } @Book{LoFaro21, author = {LoFaro, T. and Ford, J.}, publisher = {Chapman and Hall}, title = {{Discovering Dynamical Systems Through Experiment and Inquiry}}, year = {2021}, address = {Boca Raton, FL}, doi = {10.1201/9781003024132}, } @Misc{wikiIndex, author = {{Wikipedia contributors}}, title = {Index of a subgroup --- {Wikipedia, The Free Encyclopedia}}, year = {2022}, url = {https://en.wikipedia.org/wiki/Index_of_a_subgroup}, } @Article{KiLePa03, author = {Kim, Y.-O. and Lee, J. and Park, K. K.}, journal = {Pacific J. Math.}, title = {A zeta function for flip systems}, year = {2003}, pages = {289--301}, volume = {209}, doi = {10.2140/pjm.2003.209.289}, } @Misc{LC21, author = {Liang, H. and Cvitanovi{\'c}, P.}, note = {J. Phys. A 54 (2021), to appear.}, title = {A chaotic lattice field theory in one dimension}, url = {https://arxiv.org/abs/2201.11325}, } @Article{ArtMaz65, author = {Artin, M. and Mazur, B.}, journal = {Ann. Math.}, title = {On periodic points}, year = {1965}, pages = {82--99}, volume = {81}, doi = {10.2307/1970384}, } @Misc{KuScWe21, author = {K{\"u}ster, B. and Sch{\"u}tte, P. and Weich, T.}, title = {Resonances and weighted zeta functions for obstacle scattering via smooth models}, year = {2021}, doi = {10.48550/arXiv.2109.05907}, } @Book{Freidlin98, author = {Freidlin, M. I. and Wentzel, A. D.}, publisher = {Springer}, title = {{Random Perturbations of Dynamical Systems}}, year = {1998}, address = {Berlin}, doi = {10.1007/978-3-642-25847-3}, } @Comment{jabref-meta: databaseType:bibtex;}