{
  "id": "1007.0171",
  "version": "v2",
  "published": "2010-07-01T14:04:02.000Z",
  "updated": "2011-09-20T12:27:24.000Z",
  "title": "Poisson approximation for the number of visits to balls in nonuniformly hyperbolic dynamical systems",
  "authors": [
    "J. -R. Chazottes",
    "P. Collet"
  ],
  "comment": "41 pages, to appear in Ergod. Th. & Dynam. Sys",
  "categories": [
    "math.DS",
    "math.PR",
    "nlin.CD"
  ],
  "abstract": "We study the number of visits to balls B_r(x), up to time t/mu(B_r(x)), for a class of non-uniformly hyperbolic dynamical systems, where mu is the SRB measure. Outside a set of `bad' centers x, we prove that this number is approximately Poissonnian with a controlled error term. In particular, when r-->0, we get convergence to the Poisson law for a set of centers of mu-measure one. Our theorem applies for instance to the H\\'enon attractor and, more generally, to systems modelled by a Young tower whose return-time function has a exponential tail and with one-dimensional unstable manifolds. Along the way, we prove an abstract Poisson approximation result of independent interest.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-09-20T12:27:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D25",
      "60F05"
    ],
    "keywords": [
      "nonuniformly hyperbolic dynamical systems",
      "abstract poisson approximation result",
      "controlled error term",
      "independent interest",
      "poisson law"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.0171C"
    }
  }
}