{
  "id": "1704.02562",
  "version": "v1",
  "published": "2017-04-09T05:10:19.000Z",
  "updated": "2017-04-09T05:10:19.000Z",
  "title": "Phase transitions for geodesic flows and the geometric potential",
  "authors": [
    "Anibal Velozo"
  ],
  "categories": [
    "math.DS",
    "math-ph",
    "math.DG",
    "math.MP"
  ],
  "abstract": "In this paper we discuss the phenomenon of phase transitions for the geodesic flow on some geometrically finite negatively curved manifolds. We define a class of potentials going slowly to zero through the cusps of $X$ for which, modulo taking coverings, the pressure map $t\\mapsto P(tF)$ exhibits a phase transition. By careful choice of the metric at the cusp we can show that the geometric potential (or unstable jacobian) $F^{su}$ belongs to this class of potentials (modulo an additive constant). This results in particular apply for the geodesic flow on a $M$-puncture sphere for every $M\\ge 3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-09T05:10:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D35",
      "37D40"
    ],
    "keywords": [
      "geodesic flow",
      "phase transition",
      "geometric potential",
      "puncture sphere",
      "geometrically finite negatively curved manifolds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}