{
  "id": "0907.4539",
  "version": "v1",
  "published": "2009-07-27T03:12:46.000Z",
  "updated": "2009-07-27T03:12:46.000Z",
  "title": "New criteria for ergodicity and non-uniform hyperbolicity",
  "authors": [
    "F. Rodriguez Hertz",
    "Jana Rodriguez Hertz",
    "A. Tahzibi",
    "R. Ures"
  ],
  "comment": "27 pages, 6 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this work we obtain a new criterion to establish ergodicity and non-uniform hyperbolicity of smooth measures of diffeomorphisms. This method allows us to give a more accurate description of certain ergodic components. The use of this criterion in combination with topological devices such as blenders lets us obtain global ergodicity and abundance of non-zero Lyapunov exponents in some contexts. In the partial hyperbolicity context, we obtain that stably ergodic diffeomorphisms are C^1-dense among volume preserving partially hyperbolic diffeomorphisms with two-dimensional center bundle. This is motivated by a well known conjecture of C. Pugh and M. Shub.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-07-27T03:12:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D25",
      "37C40",
      "37D30"
    ],
    "keywords": [
      "non-uniform hyperbolicity",
      "partial hyperbolicity context",
      "volume preserving partially hyperbolic diffeomorphisms",
      "non-zero lyapunov exponents",
      "two-dimensional center bundle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.4539R"
    }
  }
}