{
  "id": "1310.2754",
  "version": "v2",
  "published": "2013-10-10T10:15:47.000Z",
  "updated": "2013-12-05T17:47:23.000Z",
  "title": "Statistical properties of diffeomorfisms with weak invariant manifolds",
  "authors": [
    "Jose F. Alves",
    "Davide Azevedo"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider diffeomorphisms of compact Riemmanian manifolds which have a Gibbs-Markov-Young structures, consisting of a reference set $\\Lambda$ with a hyperbolic product structure and a countable Markov partition. We assume polynomial contraction on stable leaves, polynomial backward contraction on unstable leaves, a bounded distortion property and a certain regularity of the stable foliation. We establish a control on the decay of correlations and large deviations of the SRB measure of the dynamical system, based on a polynomial control on the Lebesgue measure of the tail of return times. Finally, we present an example of a dynamical system defined on the torus and prove that it verifies the properties of the Gibbs-Markov-Young structure that we considered.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-12-05T17:47:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A05",
      "37C40",
      "37D25"
    ],
    "keywords": [
      "weak invariant manifolds",
      "statistical properties",
      "gibbs-markov-young structure",
      "diffeomorfisms",
      "hyperbolic product structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.2754A"
    }
  }
}