{
  "id": "1203.1416",
  "version": "v2",
  "published": "2012-03-07T09:45:01.000Z",
  "updated": "2012-03-11T03:29:21.000Z",
  "title": "Two remarks on $C^\\infty$ Anosov diffeomorphisms",
  "authors": [
    "Shigenori Matsumoto"
  ],
  "comment": "3 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $M$ be a closed oriented $C^\\infty$ manifold and $f$ a $C^\\infty$ Anosov diffeomorphism on $M$. We show that if $M$ is the two torus $T^2$, then $f$ is conjugate to a hyperbolic automorphism of $T^2$, either by a $C^\\infty$ diffeomorphism or by a singular homeomorphism. We also show that for general $M$, if $f$ admits an absolutely continuous invariant measure $\\mu$, then $\\mu$ is a $C^\\infty$ volume. The proofs are concatenations of well known results in the field.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-03-11T03:29:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D20"
    ],
    "keywords": [
      "anosov diffeomorphism",
      "hyperbolic automorphism",
      "singular homeomorphism",
      "absolutely continuous invariant measure",
      "concatenations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.1416M"
    }
  }
}