Week 13
ChaosBook is a book in reverse  
Group theory voodoo  
Symmetry is your friend  overview 
 25. Deterministic diffusion / 12 April 2022 /
 26. Finite groups / 14 April 2022 /
 Homework 13
 Optional
Read sect. 28.2: A class of simple 1dimensional dynamical systems where all transport coefficients can be evaluated analytically, by hand. Diffusion is a nonmonotonic function of the local expansion rate, and it is nongaussian, with a nonvanishing kurtosis. Perhaps the most fundamental diagnostic of deterministic chaos is the nondifferentiable dependence of its transport coefficients on smooth variations of system parameters.
Chapter 24 Deterministic diffusion  
Deterministic diffusion so far  a review  
Running orbits  
Cycle formulas for averages  
This is one weird formula!  
Diffusion on a 1dimensional lattice 
Finite groups. Cyclic groups of two and three elements. Symmetries of a triangle, six element group multiplication table. Matrix representations. Regular representations. This is standard material, not written up in ChaosBook, but necessary for the course. We liked Tinkham, chapter 2, or Dresselhaus chapters 1 and 2 (early version available as lecture notes).
Finite groups  slides Kezhou Lu 

Hard work builds character  
The symmetry group of a propeller  
Irreps of C3  
Rotation in the plane  
Trace of evolution operator  
?? 
diffusion Due 26 April 2022 

Discussion forum for week 13 
The deepest thing about chaos  
Why does everybody write a book on Group Theory?  
Challenge: can you quotient D6 symmetry? 