CHAOS, AND WHAT TO DO ABOUT IT  	
        ----------------------------------------------------------- 

	Georgia Tech PHYS 7123			 Fall semester 2001  
	Predrag Cvitanovic'

        Lecture 19:        11:05-12:25 Tue Oct 23 2001 in Howey N209


Dynamics, qualitative II
-----------------------
We continue learning how to count: qualitative dynamics 
of simple stretching and mixing flows is used to
introduce symbolic dynamics and Smale horseshoes.

Reading:
--------
	Classical and Quantum Chaos	---    www.nbi.dk/ChaosBook
		chapter 10 - Qualitative dynamics

Exercises: (please use current version - they will be renumbered in the
	    next version of the webbook - hopefully this weekend)
----------
        5.4 (d) Invariant measure for the ``golden mean'' map
        8.2     Spectral determinat for the ``golden mean'' map
	8.17    The Euler formula (verifies superexponential
		convergence of spectral determinants for a single
		fixed point)
	11.2    Sum of A_ij is like a trace (justifies replacing an
		average by the leading eigenvalue)
	11.3    Loop expansions (optional: important in many applications
		but perhaps not easy to prove)


         due Tue Oct 30 at 12:55