From Normal to Anomalous Deterministic Diffusion
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These lecture notes illustrate some features of deterministic transport in chaotic systems. The subject has witnessed an impressive amount of work in the last thirty years, and our review is not meant to be exhaustive, but rather focus on some unifying techniques by which the problem can be tackled, pointing out difficulties and open problems.
We start by dealing with the case of hyperbolic systems where typically normal diffusion is observed (even though actual calculation of transport coefficients may be exceedingly difficult), while the second part of the notes deals with weakly chaotic systems, where long trappings near regular phase-space regions may induce anomalies in diffusive properties. Examples of analytic calculations are given in the framework of cycle expansions, a general technique for getting chaotic averages.
KeywordsPeriodic Orbit Chaotic System Zeta Function Periodic Point Piecewise Linear Approximation
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- 10.Baladi, V. (1995): Dynamical zeta functions. In: Branner, B., Hjorth (eds) Proceedings of the NATO ASI Real and Complex Dynamical Systems. Kluwer Academic Publishers DordrechtGoogle Scholar
- 11.Devaney, R.L. (1987): An Introduction to Chaotic Dynamical Systems. Addison-Wesley Reading MAGoogle Scholar
- 12.Hansen, K.T. (1994): Symbolic Dynamics in Chaotic Systems. Ph.D. thesis, University of Oslo http://www.nbi.dk/CATS/papers/khansen/thesis/thesis.html
- 19.Lichtenberg, A.J., Lieberman, M.A. (1982): Regular and stochastic motion. Springer New YorkGoogle Scholar
- 35.Bunimovich, L.A. (1985): Decay of correlations in dynamical systems with chaotic behavior. Sov. Phys. JETP 62 842–852Google Scholar