CHAOS, AND WHAT TO DO ABOUT IT
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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
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We continue learning how to count: qualitative dynamics
of simple stretching and mixing flows is used to
introduce symbolic dynamics and Smale horseshoes.
Reading:
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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)
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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