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Correlation Decay and Recurrence Asymptotics for Some Robust Nonuniformly Hyperbolic Maps

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Abstract

We study a robust class of multidimensional non-uniformly hyperbolic transformations considered by Oliveira and Viana (Ergod. Theory Dyn. Syst. 28:501–533, 2008). For an open class of Hölder continuous potentials with small variation we show that the unique equilibrium state has exponential decay of correlations and that the distribution of hitting times is asymptotically exponential. Furthermore, using that the equilibrium states satisfy a weak Gibbs property we also prove log-normal fluctuations of the return times around their average.

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

    Paulo Varandas

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  1. Paulo Varandas
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Correspondence to Paulo Varandas.

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Varandas, P. Correlation Decay and Recurrence Asymptotics for Some Robust Nonuniformly Hyperbolic Maps. J Stat Phys 133, 813–839 (2008). https://doi.org/10.1007/s10955-008-9639-3

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  • DOI: https://doi.org/10.1007/s10955-008-9639-3

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