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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 for which the decay of the tail of the return time function can be controlled in terms of the time generic points needed 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.

Copyright 2003 American Mathematical Society

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Article Info

• ERA Amer. Math. Soc. 09 (2003), pp. 26-31
• Publisher Identifier: S 1079-6762(03)00106-9
• 2000 Mathematics Subject Classification. Primary 37D20, 37D50, 37C40
• Received by editors November 5, 2002
• Posted on February 14, 2003
• Communicated by Svetlana Katok
• Comments (When Available)

José F. Alves

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

E-mail address: jfalves@fc.up.pt

Stefano Luzzatto

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

E-mail address: stefano.luzzatto@ic.ac.uk

Vilton Pinheiro

Departamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador, Brazil

E-mail address: viltonj@ufba.br

Work carried out at the Federal University of Bahia, University of Porto and Imperial College, London. Partially supported by CMUP, PRODYN, SAPIENS and UFBA