Spectrum of dimensions for Poincaré recurrences of Markov maps

Pages: 835 - 849, Volume 8, Issue 4, October 2002

doi:10.3934/dcds.2002.8.835       Abstract        Full Text (202.9K)       Related Articles

B. Fernandez - Centre de Physique Theorique CNRS Luminy, Case 907 13288 Marseille CEDEX 09, France (email)
E. Ugalde - Instituto de Investigación en Comunicación Optica, UASLP, Av. Karakorum 1470, Lomas 4ta sección, San Luis Potosí, SLP, Mexico (email)
J. Urías - Instituto de Investigación en Comunicación Optica, UASLP, Av. Karakorum 1470, Lomas 4ta sección, San Luis Potosí, SLP, Mexico (email)

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.

Keywords:  Markov maps, Poincaré recurrences, spectra of dimensions.
Mathematics Subject Classification:  37C45.

Received: March 2001;      Revised: May 2002;      Published: July 2002.