Gibbs-Markov structures and limit laws for partially hyperbolic attractors with mostly expanding central direction |
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Authors: | José F. Alves,Vilton Pinheiro |
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Affiliation: | a Departamento de Matemática Pura, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal b Departamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador, Brazil |
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Abstract: | We consider a partially hyperbolic set K on a Riemannian manifold M whose tangent space splits as TKM=Ecu⊕Es, for which the center-unstable direction Ecu expands non-uniformly on some local unstable disk. We show that under these assumptions f induces a Gibbs-Markov structure. Moreover, the decay of the return time function can be controlled in terms of the time typical points need to achieve some uniform expanding behavior in the center-unstable direction. As an application of the main result we obtain certain rates for decay of correlations, large deviations, an almost sure invariance principle and the validity of the central limit theorem. |
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Keywords: | 37A25 37C05 37C40 37D25 37D30 |
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