{
  "id": "1212.3820",
  "version": "v1",
  "published": "2012-12-16T19:25:06.000Z",
  "updated": "2012-12-16T19:25:06.000Z",
  "title": "Non-uniform hyperbolicity and existence of absolutely continuous invariant measures",
  "authors": [
    "Javier Solano"
  ],
  "comment": "24 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that for certain partially hyperbolic skew-products, non-uniform hyperbolicity along the leaves implies existence of a finite number of ergodic absolutely continuous invariant probability measures which describe the asymptotics of almost every point. The main technical tool is an extension for sequences of maps of a result of de Melo and van Strien relating hyperbolicity to recurrence properties of orbits. As a consequence of our main result, we also obtain a partial extension of Keller's theorem guaranteeing the existence of absolutely continuous invariant measures for non-uniformly hyperbolic one dimensional maps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-12-16T19:25:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "absolutely continuous invariant measures",
      "non-uniform hyperbolicity",
      "ergodic absolutely continuous invariant probability",
      "absolutely continuous invariant probability measures",
      "leaves implies existence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.3820S"
    }
  }
}