{
  "id": "2211.16541",
  "version": "v1",
  "published": "2022-11-29T19:04:49.000Z",
  "updated": "2022-11-29T19:04:49.000Z",
  "title": "Ergodicity of the geodesic flow on symmetric surfaces",
  "authors": [
    "Michael Pandazis",
    "DragomirŠarić"
  ],
  "comment": "31 pages, 20 figures",
  "categories": [
    "math.GT",
    "math.CV"
  ],
  "abstract": "We consider conditions on the Fenchel-Nielsen parameters of a Riemann surface $X$ that guarantee the surface $X$ is of parabolic type. An interesting class of Riemann surfaces for this problem is the one with finitely many topological ends. In this case the length part of the Fenchel-Nielsen coordinates can go to infinity for {parabolic $X$}. When the surface $X$ is end symmetric, we prove that {$X$ being parabolic} is equivalent to the covering group being of the first kind. Then we give necessary and sufficient conditions on the Fenchel-Nielsen coordinates of a half-twist symmetric surface $X$ such that {$X$ is parabolic}. As an application, we solve an open question from the prior work of Basmajian, Hakobyan and the second author.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-29T19:04:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30F20",
      "30F25",
      "30F45",
      "57K20"
    ],
    "keywords": [
      "geodesic flow",
      "riemann surface",
      "ergodicity",
      "fenchel-nielsen coordinates",
      "half-twist symmetric surface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}