Geodesic
Markov structures for non-uniformly expanding maps on compact manifolds in arbitrary dimension
Alves, José1 ; Luzzatto, Stefano2 ; Pinheiro, Vilton3
1 Departamento de Matemática Pura, Faculdade de Ciências do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
2 Mathematics Department, Imperial College, 180 Queen’s Gate, London SW7, UK
3 Departamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador, Brazil
Electronic research announcements of the American Mathematical Society, Tome 09 (2003), pp. 26-31.

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S1079-6762-03-00106-9

Alves, José 1 ; Luzzatto, Stefano 2 ; Pinheiro, Vilton 3

1 Departamento de Matemática Pura, Faculdade de Ciências do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
2 Mathematics Department, Imperial College, 180 Queen’s Gate, London SW7, UK
3 Departamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador, Brazil 
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Alves, José; Luzzatto, Stefano; Pinheiro, Vilton. Markov structures for non-uniformly expanding maps on compact manifolds in arbitrary dimension. Electronic research announcements of the American Mathematical Society, Tome 09 (2003), pp. 26-31. doi : 10.1090/S1079-6762-03-00106-9. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-03-00106-9/

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