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