Spectra of dimensions for Poincaré recurrences

V. Afraimovich; J. Schmeling; Edgardo Ugalde; Jesús Urías

doi:10.3934/dcds.2000.6.901

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2000, Volume 6, Issue 4: 901-914. Doi: 10.3934/dcds.2000.6.901

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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
3.
Instituto de Física, UASLP, Alvaro Obregon 64, San Luis Potosí, SLP, 78000 México

Received: December 1999

Revised: April 2000

Published: October 2000

Abstract / Introduction Related Papers Cited by

Abstract

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.

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Mathematics Subject Classification: 37C45.

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