{
  "id": "2209.11323",
  "version": "v1",
  "published": "2022-09-22T21:30:02.000Z",
  "updated": "2022-09-22T21:30:02.000Z",
  "title": "A remark on the phase transition for the geodesic flow of a rank one surface of nonpositive curvature",
  "authors": [
    "Keith Burns",
    "Dong Chen"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "For any rank 1 nonpositively curved surface $M$, it was proved by Burns-Climenhaga-Fisher-Thompson that for any $q<1$, there exists a unique equilibrium state $\\mu_q$ for $q\\varphi^u$, where $\\varphi^u$ is the geometric potential. We show that as $q\\to 1-$, the weak$^*$ limit of $\\mu_q$ is the restriction of the Liouville measure to the regular set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-22T21:30:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D25",
      "37D40"
    ],
    "keywords": [
      "geodesic flow",
      "phase transition",
      "nonpositive curvature",
      "unique equilibrium state",
      "regular set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}