{
  "id": "1309.6539",
  "version": "v4",
  "published": "2013-09-25T15:03:30.000Z",
  "updated": "2015-03-31T12:33:57.000Z",
  "title": "On the ergodicity of geodesic flows on surfaces of nonpositive curvature",
  "authors": [
    "Weisheng Wu"
  ],
  "comment": "11 pages, 4 figures. Lemma 3.8 is added to correct a gap in the proof of Proposition 3.4. Theorem 1.5 is also added",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $M$ be a smooth compact surface of nonpositive curvature, with genus $\\geq 2$. We prove the ergodicity of the geodesic flow on the unit tangent bundle of $M$ with respect to the Liouville measure under the condition that the set of points with negative curvature on $M$ has finitely many connected components. Under the same condition, we prove that a non closed \"flat\" geodesic doesn't exist, and moreover, there are at most finitely many flat strips, and at most finitely many isolated closed \"flat\" geodesics.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-10-03T15:40:56.000Z",
      "comment": "10 pages, 4 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2015-03-31T12:33:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "geodesic flow",
      "nonpositive curvature",
      "ergodicity",
      "unit tangent bundle",
      "smooth compact surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.6539W"
    }
  }
}