{
  "id": "1112.2745",
  "version": "v1",
  "published": "2011-12-12T23:32:27.000Z",
  "updated": "2011-12-12T23:32:27.000Z",
  "title": "Hausdorff dimension of three-period orbits in Birkhoff billiards",
  "authors": [
    "Sergei Merenkov",
    "Vadim Zharnitsky"
  ],
  "comment": "10 pages, 1 figure",
  "categories": [
    "math.DS",
    "nlin.CD"
  ],
  "abstract": "We prove that the Hausdorff dimension of the set of three-period orbits in classical billiards is at most one. Moreover, if the set of three-period orbits has Hausdorff dimension one, then it has a tangent line at almost every point.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-12-12T23:32:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E99"
    ],
    "keywords": [
      "three-period orbits",
      "hausdorff dimension",
      "birkhoff billiards"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/0951-7715/25/7/1947",
      "journal": "Nonlinearity",
      "year": 2012,
      "month": "Jul",
      "volume": 25,
      "number": 7,
      "pages": 1947
    },
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012Nonli..25.1947M"
    }
  }
}