17 July 1998

All problem sets and solutions listed here have been incorporated in the exercises and solutions in the main text of the webbook.

Last updated 7 April 1997

Geometry of chaos - 1996 problem sets

Problem set 1
A few problems to get warmed up. If you only do one of them, do the determinant is the exponential of the trace of the log.
Problem set 2
Problems related to the definition of dynamical systems. Also the first problems related to symbolic dynamics.
Problem set 3
Problems related to ergodic behavior. A prelude to the operators that will come in the next set.
Problem set 4
First set of problems related to spectral determinants and one on computing the invariant measure for a map.
Problem set 5
A few specific examples in using spectral determinants. Re-known for what it is not.
Problem set 6
The Euler formula, our first spectral determinant, and a numerical escape rate.
Problem set 7
A few warm up problems in using spectral determinants.
Problem set 8
Computing averages and properties of fractals.
Problem set 9
Billiards. The last problem of allows to estimate the entropy of the Bunimovich stadium quite well. It can be done with little algebra, but requires some giant leaps of faith.
Problem set 10
Recycling Ising-like spin systems.
Problem set 11
Quantum mechanics. These are the Jacobi gymnastics and two-d billiard problems for quantum cycles.
Problem set 12
More quantum mechanics. The two disk problem via cycles and the scattering.
Problem set 13
Discrete symmetries: properties of group of symmetries of the triangle, factorizing the Ising model, and the small determinant in cycle expansions.

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