Week 10
Week 10 overview  
Think locally, act globally: A lightning review 
 19. Transporting densities
 20. Averaging
 Homework 10
 Optional
Chapter 19 Transporting densities Skip sects. 19.3 and 19.6. 

A first attempt to move the whole phase space around  natural measure and fancy operators.  
What is a measure?  
PerronFrobenius operator  
Dirac delta function  get used to it  
Invariant measure  
Ergodic measure  
What do I measure? Observables  
Evolution in infinitesimal time 
Chapter 20 Averaging Read sects. 20.1 and 20.2. Skip sect. 20.1.3 "Moments, cumulants" 

Averaging  slides Jemma Fendley 

On the necessity of studying the averages of observables in chaotic dynamics. Formulas for averages are cast in a multiplicative form that motivates the introduction of evolution operators. Discretetime and generating functions continued and compared. Infinitesimal time evolution related to the infinite time dynamics via a Laplace transform. The stage is set for the classical trace formula.  
Idea: Globallocal duality  
Idea: PerronFrobenius operator  
Time averages of observables  
State space averages of observables  
A simple idea: Exponentiate!  
Evolution operator  
Evolution operators form a semigroup  
Spectra of evolution operators 
Natural measure Due 3 April 2022 

Discussion forum for week 10 