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Pré-Publication, Document De Travail Année : 2014

Poisson law for some nonuniformly hyperbolic dynamical systems with polynomial rate of mixing

Résumé

We consider some nonuniformly hyperbolic invertible dynamical systems which are modeled by a Gibbs-Markov-Young tower. We assume a polynomial tail for the inducing time and a polynomial control of hyperbolicity, as introduced by Alves, Pinheiro and Azevedo. These systems admit a physical measure with polynomial rate of mixing. In this paper we prove that the distribution of the number of visits to a ball B(x, r) converges to a Poisson distribution as the radius r → 0 and after suitable normalization.
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hal-00931130 , version 1 (14-01-2014)

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Françoise Pene, Benoit Saussol. Poisson law for some nonuniformly hyperbolic dynamical systems with polynomial rate of mixing. 2014. ⟨hal-00931130⟩
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