So far there are 3 cycle finding programs in this directory:

logistic_simple.f 
finds cycles of the logistic map f(x)=4.5*x*(1-x) from the input cycle 
length, q, and initial guess, x(i),i=1,q. It is easy to change this program
to find cycles of any other 1-d map; just change the subroutine map.


logistic_total.f
finds all cycles of length between q1 and q2 (the only input). This means
that the program produces symbol sequences for all prime cycles. This
section of the program is not overly commented, but it might be worthwhile
to understand this part of the program if you are not totally conversant
in the mysteries of symbolic dynamics. The example is as above the
logistic map, so the symbolic dynamics is binary. If you change the program
to find cycles of some other map then you have to change
  the subroutine map (surprisingly)
  the initial guess (I have used simply x=.2 for symbol 0 and x=.8 for symbol
1. Even if you just lower the parameter r of the logistic map to cases
where the symbolic dynamics is pruned you may have to change this part
of the program.
  the symbolic dynamics - if you change to something other than binary 
dynamics, for example the trinary dynamics of a bimodal map.


henon_simple.f
a 2-d version of logistic_simple.f. The example map is the Henon map
f(x,y)=(a-x**2+b*y,x), a=1,4, b=.3 (this may be a slightly different
version from what is given in the QCcourse lecture notes, but that is
just a matter of a simple rescaling of the variables.)
Everything in henon_simple.f is the same as logistic_simple.f except that
where in the latter we deal with just numbers, in the former some of these
numbers have become 2-d vectors, others 2x2 matrices. From this program it
is easy to generalize to higher-d maps.

programs to come: 
cycles of an ODE (probably Roessler or Lorentz)
cycles of a Hamiltonian system (co-linear Helium is the choice of the
  powers that be)
super-Henon program (finds all cycles of the Henon map and produces the
  pruning front along the way)


28/10-96 Freddy Christiansen (freddy@alf.nbi.dk)

 
