Spectrum of dimensions for Poincaré recurrences of Markov maps

B. Fernandez; E. Ugalde; J. Urías

doi:10.3934/dcds.2002.8.835

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2002, Volume 8, Issue 4: 835-849. Doi: 10.3934/dcds.2002.8.835

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Spectrum of dimensions for Poincaré recurrences of Markov maps

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

Received: March 2001

Revised: May 2002

Published: October 2002

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Abstract

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.

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Mathematics Subject Classification: 37C45.

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