Simple Maps with Fractal Diffusion Coefficients

Preprint

16 December 1994

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.chao-dyn/9407018

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.

Keywords

DIFFUSION COEFFICIENT
FRACTAL DIFFUSION
CONSIDER CHAINS
CHAOTIC MAPS
EIGENVALUES
SIMPLE MAPS
SLOPE

All Related Versions

Version 1, 1994-08-03, ArXiv
Version 2, 1994-12-16, ArXiv
Published version: Physical Review Letters, 74 (3), 387.

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