{
  "id": "1812.00377",
  "version": "v1",
  "published": "2018-12-02T12:13:41.000Z",
  "updated": "2018-12-02T12:13:41.000Z",
  "title": "On the mixing and Bernoulli properties for geodesic flows on rank 1 manifolds without focal points",
  "authors": [
    "Fei Liu",
    "Xiaokai Liu",
    "Fang Wang"
  ],
  "comment": "19 pages, 1 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "If $(M,g)$ is a smooth compact rank $1$ Riemannian manifold without focal points, it is shown that the measure $\\mu_{\\max}$ of maximal entropy for the geodesic flow is unique. In this article, we study the statistic properties and prove that this unique measure $\\mu_{\\max}$ is mixing. Stronger conclusion that the geodesic flow on the unit tangent bundle $SM$ with respect to $\\mu_{\\max}$ is Bernoulli is acquired provided $M$ is a compact surface with genus greater than one and no focal points.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-02T12:13:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B40",
      "37D40"
    ],
    "keywords": [
      "geodesic flow",
      "focal points",
      "bernoulli properties",
      "smooth compact rank",
      "unit tangent bundle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}