Fractal diffusion coefficient from dynamical zeta functions

Details Fractal diffusion coefficient from dynamical zeta functions Fractal diffusion coefficient from dynamical zeta functions

2005-09-28

arxiv.org/abs/nlin/0509051v1

J. Phys. A: Math. Gen. 39 L151-L157 2006

Nonlinear Sciences

Chaotic Dynamics

8 pages, 2 figures

Scientific paper

10.1088/0305-4470/39/10/L01

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.

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