Simple Maps with Fractal Diffusion Coefficients

R. Klages; J. R. Dorfman

doi:10.1103/physrevlett.74.387

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arXiv · chao-dyn/9407018

Simple Maps with Fractal Diffusion Coefficients

R. Klages·J. R. Dorfman

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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.

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R. Klages, J. R. Dorfman. 1994-12-16. Simple Maps with Fractal Diffusion Coefficients. https://doi.org/10.1103/physrevlett.74.387

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