Simple Maps with Fractal Diffusion Coefficients

Abstract

We consider chains of one-dimensional, piecewise linear, chaotic maps with uniform slope. We study the diffusive behaviour of an initially nonuniform distribution of points as a function of the slope of the map by solving Frobenius-Perron equation. For Markov partition values of the slope, we relate the diffusion coefficient to eigenvalues of the topological transition matrix. The diffusion coefficient obtained shows a fractal structure as a function of the slope of the map. This result may be typical for a wide class of maps, such as two dimensional sawtooth maps.

4 pages, LaTeX with REVTeX, and 3 figures, Postscript, in uuencoded tar file. to appear in Phys. Rev. Lett

References in corpus (3)

• Steady-State Electrical Conduction in the Periodic Lorentz Gas
• Periodic Orbit Theory of Anomalous Diffusion
• The Topological Entropy of One-dimensional Maps: Approximations and Bounds

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