Fractal properties of the diffusion coefficient in a simple deterministic dynamical system: a numerical study

Details Fractal properties of the diffusion coefficient in a simple deterministic dynamical system: a numerical study Fractal properties of the diffusion coefficient in a simple deterministic dynamical system: a numerical study

2004-03-15

arxiv.org/abs/nlin/0403026v1

Acta Physica Polonica B 35, 1365 (2004)

Nonlinear Sciences

Chaotic Dynamics

10 pages, 4 eps figures, to appear in Acta Physica Polonica B (2004) at http://th-www.if.uj.edu.pl/acta/

Scientific paper

Using a numerical library for arbitrary precision arithmetic I study the irregular dependence of the diffusion coefficient on the slope of a piecewise linear map defining a dynamical system. I find that the graph of the diffusion coefficient as a function of the slope has the fractal dimension 1, but the convergence to this limit is slowed down by logarithmic corrections. The exponent controlling this correction depends on the slope and is either 1 or 2 depending on existence and properties of a Markov partition.

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