Fractal diffusion coefficient from dynamical zeta functions

Abstract

Dynamical zeta functions provide a powerful method to analyze low dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand even simple one dimensional maps can show an intricate structure of the grammar rules that may lead to a non smooth dependence of global observable on parameters changes. A paradigmatic example is the fractal diffusion coefficient arising in a simple piecewise linear one dimensional map of the real line. Using the Baladi-Ruelle generalization of the Milnor-Thurnston kneading determinant we provide the exact dynamical zeta function for such a map and compute the diffusion coefficient from its smallest zero.

8 pages, 2 figures

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Cited by in corpus (6)

• Fractal Properties of Anomalous Diffusion in Intermittent Maps
• Dependence of chaotic diffusion on the size and position of holes
• Continuity properties of transport coefficients in simple maps
• Follow the fugitive: an application of the method of images to open dynamical systems
• Linear and fractal diffusion coefficients in a family of one dimensional chaotic maps
• Capturing correlations in chaotic diffusion by approximation methods