Week 6
Week 6 overview 
 11. Slice and dice / 13 February 2018 /
 11. Qualitative dynamics for pedestrians / 15 February 2018 /
 Homework 6
 Optional
Actions of a Lie group on a state trace out a manifold of equivalent states, or its group orbit. Symmetry reduction is the identification of a unique point on a group orbit as the representative of this equivalence class. Thus, if the symmetry is continuous, the interesting dynamics unfolds on a lowerdimensional `quotiented', or `reduced' state space M/G. In the method of slices the symmetry reduction is achieved by cutting the group orbits with a set of hyperplanes, one for each continuous group parameter, with each group orbit of symmetryequivalent points represented by a single point, its intersection with the slice. Moving frames give us a great deal of freedom  we discuss how to choose a frame The most natural of all moving frames: the comoving frame, the frame for space cowboys.
Chapter Slice & dice Read Sects. 13.4 and 13.5. The rest is optional. 

Overheads  
Symmetry reduction NBB  
Symmetry reduced equations of motion  
Sections and slices are local, good up to a border  
A spatial Fourier expansion NBB  
First Fourier mode slice NBB  
Inslice time NBB  
Comoving frames As of 2 Mar 2015, exists only as a video, this is not yet written up in ChaosBook The most natural of all moving frames: the comoving frame, the frame for space cowboys. 
Qualitative properties of a flow partition the state space in a topologically invariant way.
Symbolic dynamics Due 27 February 2018 

Discussion forum for week 6 
Master Slicer Certificate  
Ring of Fire Visualize the O(2) equivariance of KuramotoSivashinsky (AKA Ring of Fire) 