{
  "id": "1805.11743",
  "version": "v1",
  "published": "2018-05-29T23:38:48.000Z",
  "updated": "2018-05-29T23:38:48.000Z",
  "title": "Convergence of spherical averages for actions of Fuchsian Groups",
  "authors": [
    "Alexander I. Bufetov",
    "Alexey Klimenko",
    "Caroline Series"
  ],
  "comment": "56 pages, 12 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "Pointwise convergence of spherical averages is proved for a measure-preserving action of a Fuchsian group. The proof is based on a new variant of the Bowen-Series symbolic coding for Fuchsian groups that, developing a method introduced by Wroten, simultaneously encodes all possible shortest paths representing a given group element. The resulting coding is self-inverse, giving a reversible Markov chain to which methods previously introduced by the first author for the case of free groups may be applied.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-29T23:38:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20H10",
      "22D40",
      "37A30"
    ],
    "keywords": [
      "fuchsian group",
      "spherical averages",
      "convergence",
      "first author",
      "reversible markov chain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 56,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}