{
  "id": "1401.3599",
  "version": "v1",
  "published": "2014-01-15T14:12:43.000Z",
  "updated": "2014-01-15T14:12:43.000Z",
  "title": "Poisson law for some nonuniformly hyperbolic dynamical systems with polynomial rate of mixing",
  "authors": [
    "Francoise Pene",
    "Benoit Saussol"
  ],
  "comment": "21 pages, 3 figures",
  "categories": [
    "math.DS"
  ],
  "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 $\\to$ 0 and after suitable normalization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-15T14:12:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonuniformly hyperbolic dynamical systems",
      "polynomial rate",
      "poisson law",
      "poisson distribution",
      "nonuniformly hyperbolic invertible dynamical systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.3599P"
    }
  }
}