Week 4
week 4 overview 
 7. Discrete symmetries of dynamics / 30 January 2018 /
 8. Discrete symmetry reduction of dynamics to a fundamental domain / 1 February 2018 /
 Homework 4
 Optional
What is a symmetry of laws of motion? The families of symmetryrelated full state space cycles are replaced by fewer and often much shorter "relative" cycles, and the notion of a prime periodic orbit is replaced by the notion of a "relative" periodic orbit, the shortest segment that tiles the cycle under the action of the group. Discrete symmetries: a review of the theory of finite groups.
While everyone can visualize the fundamental domain for a 3disk billiard, the simpler problem  symmetry reduction of 1d dynamics that is equivariant under a reflection, the most common symmetry in applications  seems to baffle everyone. So here is a stepbystep walk through to this simplest of all symmetry reductions.
Chapter 11 World in a mirror  
Chapter 11 overheads  
Fundamental domain still redoing videos for this week. 
discrete symmetry reduction Due 13 February 2018 

Discussion forum for week 5 
Handwritten: a 1dimensional fundamental domain  
"It does not say anyplace in the Bible that if equations of motion have a symmetry, solutions should have it too." 