Level: MSci, MSc
Title: Deterministic chaos in the Baker map
Supervisor:

Dr Rainer Klages
Research Area: Dynamical Systems and Statistical Physics
Description:

Style and difficulty:

  • Textbook-based, but requires to learn about some concepts that are more demanding than for the project Deterministic chaos in the Bernoulli shift. Could again be purely analytical or in combination with computer work. Again, will be difficult, though not impossible, to score an A with it. If done well should be safe for an (upper) B.

Contents:

  • The baker map is perhaps the simplest two-dimensional map exhibiting chaotic behaviour. Based on different textbooks, summarize important dynamical systems properties of this paradigmatic model such as its dynamical instability, ergodicity, mixing behaviour, being a K-system, and being Bernoulli. This requires to calculate analytically Lyapunov exponents, dynamical entropies and to use symbolic dynamics. Finally, construct analytically the SRB measure for a dissipative baker's map. If you like, also discuss Arnold's cat map. You may support your analytical results by computer simulations.
Further Reading:
  • J.R. Dorfman, An Introduction to Chaos in Nonequilibrium Statistical Mechanics. Cambridge Univ. Press, 1999.
  • V.I. Arnold and A. Avez, Ergodic problems of classical mechanics. W.A. Benjamin, New York, 1968.
  • M.Toda, R.Kubo, and N.Saito, Statistical Physics 1. Springer, Berlin, 1992.
  • A. Lasota and M.C. Mackey, Chaos, Fractals, and Noise. Springer, Berlin, 1994.
  • T. Tel and M. Gruiz, Chaotic Dynamics. Cambridge Univ. Press, 2006.
Key Modules:

MTH6107 Chaos and Fractals

MTH744U/MTH744P Dynamical Systems

MTH743U/MTH743P Complex Systems
Other Information:

This is a project about dynamical systems theory, hence you should have interest and some working knowledge of this theory as provided by at least one of the modules above.
Current Availability: Yes