{
  "id": "1610.01870",
  "version": "v1",
  "published": "2016-10-06T13:41:00.000Z",
  "updated": "2016-10-06T13:41:00.000Z",
  "title": "Hausdorff Dimension of Non-Diophantine Points in Finite-Volume Quotients of Rank One Semisimple Lie Groups",
  "authors": [
    "Cheng Zheng"
  ],
  "comment": "40 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this note, we give a definition of Diophantine points of type $\\gamma$ for $\\gamma\\geq0$ in a homogeneous space $G/\\Gamma$ and we compute Hausdorff dimensions of subsets of points which are not Diophantine of type $\\gamma$ when $G$ is a semisimple Lie group of real rank one. As a corollary, we will give a description of Hausdorff dimensions of non-Diophantine points of various types in Heisenberg groups, which could be considered as a Jarnik-Besicovitch Theorem on Diophantine approximation in Heisenberg groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-06T13:41:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E40",
      "37A17"
    ],
    "keywords": [
      "semisimple lie group",
      "hausdorff dimension",
      "non-diophantine points",
      "finite-volume quotients",
      "heisenberg groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}