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Unformatted text preview: Lecture 41: Chaos I (9 Dec 09) Final exam: take home distributed Dec 14, due 1PM Dec 21, limit 72 hours of work. Review 7 Dec homework A. Introduction 1. Ref linked to text: Fetter and Walecka, Nonlinear Mechanics (Sup- plement) (Dover 2006) with course reserves in Physics library. 2. Refs: Goldstein Chapter 11, special issue: Chaos (journal, Vol 15, #1 2005) on FPU (Fermi-Pasta-Ulam) problem. 3. Work on Newtonian classical mechanics that developed into modern turbulence theory. 4. Some quotes: R. M. May (1) simple nonlinear systems do not necessar- ily possess simple dynamical properties (2) wide classes of determin- istic models can give rise to apparently chaotic dynamical behavior; M. Feigenbaum some very simple schemes [deterministic] to produce erratic numbers behave identically to some of the erratic aspects of natural phenomena; J. Ford, coexistence of apparently random and apparently deterministic behavior. 5. Such issues arise for the foundations of stat mech: question of the extent to which trajectories in multi-dim space (many degrees of freedom) will sample phase space thoroughly and thus support the replacement of time average by phase average. Also will address the approach to equilibrium. 6. Math analysis on stability in nonlinear mechanics KAM (Kolmogorov- Arnold-Moser) theorem.Arnold-Moser) theorem....
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- Fall '09