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From Deterministic Chaos to Deterministic Diffusion

Author: R. Klages (Queen Mary, University of London)
Url: http://arxiv.org/abs/0804.3068
Format: Pdf
Year: 2008
Category: Dynamical Systems
Pages: 36
Clicks: 2322

This is a set of easy-to-read lecture notes for a short first-year Ph.D. student course on Applied Dynamical Systems, which was given at the London Taught Course Centre in Spring 2008. The notes cover five hours of lectures and do not require any preknowledge on dynamical systems. The first part introduces to deterministic chaos in one-dimensional maps in form of Ljapunov exponents and the metric entropy. The second part first outlines the concept of deterministic diffusion. Then the escape rate formalism for deterministic diffusion, which expresses the diffusion coefficient in terms of the above two chaos quantities, is worked out for a simple map. The notes conclude with a very brief sketch of anomalous diffusion.

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