Poisson law for some nonuniformly hyperbolic dynamical systems with polynomial rate of mixing 2014-02-05 11:30 Dynamical Systems Hyperbolic Polyhedric Billiards 2014-01-24 14:30 Dynamical Systems Automaticity, finite complete rewriting systems, and fin

  We consider some nonuniformly hyperbolic invertible dynamical system 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 successive entrances times into a ball $B(x,r)$ converges to a Poisson distribution as the radius $r\to0$ and after suitable normalization.