Spectrum of dimensions for Poincaré recurrences of Markov maps

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November 2002, 8(4): 835-849. doi: 10.3934/dcds.2002.8.835

Spectrum of dimensions for Poincaré recurrences of Markov maps

B. Fernandez ^1, , E. Ugalde ^2, and J. Urías ^2,

1.	Centre de Physique Theorique CNRS Luminy, Case 907 13288 Marseille CEDEX 09, France
2.	Instituto de Investigación en Comunicación Optica, UASLP, Av. Karakorum 1470, Lomas 4ta sección, San Luis Potosí, SLP, Mexico, Mexico

Received March 2001 Revised May 2002 Published July 2002

Abstract
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The spectrum of dimensions for Poincaré recurrences of Markov maps is obtained by constructing a sequence of approximating maps whose spectra are known to be solution of non-homogeneous Bowen equations. We prove that the spectrum of the Markov map also satisfies such an equation.

Keywords: Markov maps, Poincaré recurrences, spectra of dimensions..

Mathematics Subject Classification: 37C4.

Citation: B. Fernandez, E. Ugalde, J. Urías. Spectrum of dimensions for Poincaré recurrences of Markov maps. Discrete & Continuous Dynamical Systems - A, 2002, 8 (4) : 835-849. doi: 10.3934/dcds.2002.8.835

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