{
  "id": "1410.7707",
  "version": "v1",
  "published": "2014-10-28T17:27:24.000Z",
  "updated": "2014-10-28T17:27:24.000Z",
  "title": "Conservative anosov diffeomorphisms of the two torus without an absolutely continuous invariant measure",
  "authors": [
    "Zemer Kosloff"
  ],
  "comment": "64 pages, 7 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We construct examples of $C^{1}$ Anosov diffeomorphisms on $\\mathbb{T}^{2}$ which are of Kreiger type ${\\rm III}_{1}$ with respect to Lebesgue measure. This shows that the Gurevic Oseledec phenomena that conservative $C^{1+\\alpha}$ Anosov diffeomorphisms have a smooth invariant measure does not hold true in the $C^{1}$ setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-28T17:27:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D20",
      "37C40",
      "37A40"
    ],
    "keywords": [
      "absolutely continuous invariant measure",
      "conservative anosov diffeomorphisms",
      "gurevic oseledec phenomena",
      "smooth invariant measure",
      "kreiger type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 64,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.7707K"
    }
  }
}