Markov structures and decay of correlations for non-uniformly expanding dynamical systems
José F. AlvesDepartamento de Matemática Pura, Faculdade de Ciências do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
Stefano LuzzattoMathematics Department, Imperial College, 180 Queen's Gate, London SW7, UK
Vilton PinheiroDepartamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador, Brazil
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. 817–839DOI 10.1016/J.ANIHPC.2004.12.002