CHAOS, AND WHAT TO DO ABOUT IT
-----------------------------------------------------------
Georgia Tech PHYS 7123 Fall semester 2001
Predrag Cvitanovic'
Lecture 21: 11:05-12:25 Tue Oct 30 2001 in Howey N209
Counting
--------
We finish learning how to count: the traces of powers of the
transition matrix count admissible cycles, and the largest eigenvalue of
the transition matrix yields the topological entropy. The secular determinant
of the transition matrix - the Artin-Mazur zeta function - is expressed
in terms of the loops of a Markov diagram.
By now we have covered for the first time the whole distance from diagnosing
chaotic dynamcs to computing zeta functions. Historically, these topological
zeta functions were the inspiration for injecting statistical mechanics
into computation of dynamical averages; Ruelle's zeta functions are a weighted
generalization of the counting zeta functions.
Reading:
--------
Classical and Quantum Chaos --- www.nbi.dk/ChaosBook
chapter 11 - Counting
Exercises: (please use current version - some exercises have been
renumbered)
----------
due Tue ?? at 12:55