{
  "id": "1912.07825",
  "version": "v1",
  "published": "2019-12-17T05:24:53.000Z",
  "updated": "2019-12-17T05:24:53.000Z",
  "title": "Properties of equilibrium states for geodesic flows over manifolds without focal points",
  "authors": [
    "Dong Chen",
    "Lien-Yung Kao",
    "Kiho Park"
  ],
  "comment": "Comments are welcome",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that for closed rank 1 manifolds without focal points the equilibrium states are unique for H\\\"older potentials satisfying the pressure gap condition. In addition, we provide a criterion for a continuous potential to satisfy the pressure gap condition. Moreover, we derive several ergodic properties of the unique equilibrium states including the equidistribution and the K-property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-17T05:24:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "focal points",
      "geodesic flows",
      "pressure gap condition",
      "unique equilibrium states",
      "ergodic properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}