JournalsaihpcVol. 22, No. 6pp. 817–839

Markov structures and decay of correlations for non-uniformly expanding dynamical systems

  • José F. Alves

    Departamento de Matemática Pura, Faculdade de Ciências do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal

  • Stefano Luzzatto

    Mathematics Department, Imperial College, 180 Queen's Gate, London SW7, UK

  • Vilton Pinheiro

    Departamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador, Brazil
Markov structures and decay of correlations for non-uniformly expanding dynamical systems cover
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Abstract

We consider non-uniformly expanding maps on compact Riemannian manifolds of arbitrary dimension, possibly having discontinuities and/or critical sets, and show that under some general conditions they admit an induced Markov tower structure. Moreover, the decay of the return time function can be controlled in terms of the time generic points need to achieve some uniform expanding behavior. As a consequence we obtain some rates for the decay of correlations of those maps and conditions for the validity of the Central Limit Theorem.

Cite this article

José F. Alves, Stefano Luzzatto, Vilton Pinheiro, Markov structures and decay of correlations for non-uniformly expanding dynamical systems. Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (2005), no. 6, pp. 817–839

DOI 10.1016/J.ANIHPC.2004.12.002