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

Transporting densities Updated 9 March 2015 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 Updated 9 March 2015 Read sects. 20.1 and 20.2. Skip sect. 20.1.3 "Moments, cumulants" 

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  
Discussion forum for week 10 