{
  "id": "math/0404433",
  "version": "v1",
  "published": "2004-04-23T16:15:20.000Z",
  "updated": "2004-04-23T16:15:20.000Z",
  "title": "Hausdorff dimension of the set of nonergodic directions (with an appendix by M. Boshernitzan)",
  "authors": [
    "Yitwah Cheung"
  ],
  "comment": "18 pages published version",
  "journal": "Ann. of Math. (2), Vol. 158 (2003), no. 2, 661--678",
  "categories": [
    "math.DS",
    "math.NT"
  ],
  "abstract": "It is known that nonergodic directions in a rational billiard form a subset of the unit circle with Hausdorff dimension at most 1/2. Explicit examples realizing the dimension 1/2 are constructed using Diophantine numbers and continued fractions. A lower estimate on the number of primitive lattice points in certain subsets of the plane is used in the construction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-04-23T16:15:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonergodic directions",
      "hausdorff dimension",
      "boshernitzan",
      "rational billiard form",
      "unit circle"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Princeton University and the Institute for Advanced Study",
      "journal": "Ann. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......4433C"
    }
  }
}