October  2000, 6(4): 901-914. doi: 10.3934/dcds.2000.6.901

Spectra of dimensions for Poincaré recurrences

1. 

IICO-UASLP, A. Obregón 64, 78000 San Luis Postosí, SLP

2. 

Fachbereich Mathematik und Informatik, Freie Universität Berlin, Arnimallee 2-6, D-14195 Berlin, Germany

3. 

Instituto de Física, UASLP, Alvaro Obregon 64, San Luis Potosí, SLP, 78000 México, Mexico, Mexico

Received  December 1999 Revised  April 2000 Published  August 2000

The spectra of Poincaré recurrences for two classes of dynamical systems are obtained in the framework of the Carathéodory construction. One class contains systems which are topologically conjugate to subshifts with the specification property, the other consists of minimal multipermutative symbolic systems. The spectra are shown to be solutions of a non-homogeneous Bowen equation, and their relationship with multifractal spectra of Lyapunov exponents is exposed.
Citation: V. Afraimovich, J. Schmeling, Edgardo Ugalde, Jesús Urías. Spectra of dimensions for Poincaré recurrences. Discrete and Continuous Dynamical Systems, 2000, 6 (4) : 901-914. doi: 10.3934/dcds.2000.6.901
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