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Electronic Research Announcements
ISSN 1079-6762

Markov structures for non-uniformly expanding maps on compact manifolds in arbitrary dimension


Authors: José F. Alves, Stefano Luzzatto and Vilton Pinheiro
Journal: Electron. Res. Announc. Amer. Math. Soc. 9 (2003), 26-31
MSC (2000): Primary 37D20, 37D50, 37C40
Published electronically: February 14, 2003
MathSciNet review: 1988869
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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 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.


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Additional Information

José F. Alves
Affiliation: Departamento de Matemática Pura, Faculdade de Ciências do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
Email: jfalves@fc.up.pt

Stefano Luzzatto
Affiliation: Mathematics Department, Imperial College, 180 Queen’s Gate, London SW7, UK
Email: stefano.luzzatto@ic.ac.uk

Vilton Pinheiro
Affiliation: Departamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador, Brazil
Email: viltonj@ufba.br

DOI: http://dx.doi.org/10.1090/S1079-6762-03-00106-9
PII: S 1079-6762(03)00106-9
Received by editor(s): November 5, 2002
Published electronically: February 14, 2003
Additional Notes: Work carried out at the Federal University of Bahia, University of Porto and Imperial College, London. Partially supported by CMUP, PRODYN, SAPIENS and UFBA
Communicated by: Svetlana Katok
Article copyright: © Copyright 2003 American Mathematical Society