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

2014/01/15 by Françoise Pène, Benoît Saussol, Pene, Francoise +1 · 3 citations
Mathematics · #Mathematical Dynamics and Fractals #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1401.3599

Abstract

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.

Citations

• Recurrence times and rates of mixing
• Statistical Properties of Dynamical Systems with Some Hyperbolicity

Cited by

• Return Times Distribution of Expanding Maps
• Hitting times distribution and extreme value law for flows
• Entry times distribution for dynamical balls on metric spaces

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