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
- 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.
Predrag Cvitanovic',
predrag@nbi.dk