{
  "id": "1903.09831",
  "version": "v1",
  "published": "2019-03-23T15:15:14.000Z",
  "updated": "2019-03-23T15:15:14.000Z",
  "title": "Uniqueness of the measure of maximal entropy for geodesic flows on certain manifolds without conjugate points",
  "authors": [
    "Vaughn Climenhaga",
    "Gerhard Knieper",
    "Khadim War"
  ],
  "comment": "35 pages, 4 figures",
  "categories": [
    "math.DS",
    "math.DG"
  ],
  "abstract": "We prove that for closed surfaces $M$ with Riemannian metrics without conjugate points and genus $\\geq 2$ the geodesic flow on the unit tangent bundle $T^1M$ has a unique measure of maximal entropy. Furthermore, this measure is fully supported on $T^1M$ and the flow is mixing with respect to this measure. We formulate conditions under which this result extends to higher dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-23T15:15:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "geodesic flow",
      "maximal entropy",
      "conjugate points",
      "uniqueness",
      "unit tangent bundle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}