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