Simple Maps with Fractal Diffusion Coefficients
chao-dyn
2009-10-22 v2 Chaotic Dynamics
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.
Cite
@article{arxiv.chao-dyn/9407018,
title = {Simple Maps with Fractal Diffusion Coefficients},
author = {R. Klages and J. R. Dorfman},
journal= {arXiv preprint arXiv:chao-dyn/9407018},
year = {2009}
}
Comments
4 pages, LaTeX with REVTeX, and 3 figures, Postscript, in uuencoded tar file. to appear in Phys. Rev. Lett