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.
Publié le : 2014-01-14
Classification:
poisson distribution,
quantitative recurrence,
Young tower,
polynomial rate,
nonuniform hyperbolicity,
billiard,
stadium,
MSC 37B20,
[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]
@article{hal-00931130,
author = {Pene, Fran\c coise and Saussol, Benoit},
title = {Poisson law for some nonuniformly hyperbolic dynamical systems with polynomial rate of mixing},
journal = {HAL},
volume = {2014},
number = {0},
year = {2014},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00931130}
}
Pene, Françoise; Saussol, Benoit. Poisson law for some nonuniformly hyperbolic dynamical systems with polynomial rate of mixing. HAL, Tome 2014 (2014) no. 0, . http://gdmltest.u-ga.fr/item/hal-00931130/