{
  "id": "1112.6023",
  "version": "v2",
  "published": "2011-12-27T21:03:39.000Z",
  "updated": "2012-08-20T08:05:32.000Z",
  "title": "Example of a diffeomorphism for which the special ergodic theorem doesn't hold",
  "authors": [
    "Dmitry Ryzhov"
  ],
  "comment": "15 pages, 7 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this work we present an example of C^\\infty-diffeomorphism of a compact 4-manifold such that it admits a global SRB measure \\mu but for which the special ergodic theorem doesn't hold. Namely, for this transformation there exist a continuous function \\phi and a positive constant \\alpha such that the following holds: the set of the initial points for which the Birkhoff time averages of the function \\phi differ from its \\mu--space average by at least \\alpha has zero Lebesgue measure but full Hausdorff dimension.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-08-20T08:05:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D20",
      "37A25",
      "37A50"
    ],
    "keywords": [
      "special ergodic theorem",
      "diffeomorphism",
      "global srb measure",
      "birkhoff time averages",
      "zero lebesgue measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.6023R"
    }
  }
}