Slow Rates of Mixing for Dynamical Systems with Hyperbolic Structures |
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Authors: | José F Alves Vilton Pinheiro |
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Institution: | (1) Departamento de Matemática Pura, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal;(2) Departamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador, Brazil |
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Abstract: | We consider invertible discrete-time dynamical systems having a hyperbolic product structure in some region of the phase space
with infinitely many branches and variable return time. We show that the decay of correlations of the SRB measure associated
to that hyperbolic structure is related to the tail of the recurrence times. We also give sufficient conditions for the validity
of the Central Limit Theorem. This extends previous results by Young in (Ann. Math. 147: 585–650, 1998]; Israel J. Math. 110: 153–188, 1999]).
Work carried out at the Federal University of Bahia, University of Porto and IMPA. J.F.A. was partially supported by FCT through
CMUP and POCI/MAT/61237/2004. V.P. was partially supported by PADCT/CNPq and POCI/MAT/61237/2004. |
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Keywords: | Recurrence times Decay of correlations Central limit theorem |
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