Dynamical zeta functions provide a powerful method to analyse 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 observables 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.

G. Cristadoro (2006). Fractal diffusion coefficient from dynamical zeta functions. JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL, 39, L151-L157 [10.1088/0305-4470/39/10/L01].

Fractal diffusion coefficient from dynamical zeta functions

CRISTADORO, GIAMPAOLO
2006

Abstract

Dynamical zeta functions provide a powerful method to analyse 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 observables 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.
2006
G. Cristadoro (2006). Fractal diffusion coefficient from dynamical zeta functions. JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL, 39, L151-L157 [10.1088/0305-4470/39/10/L01].
G. Cristadoro
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/98977
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