{
  "id": "math/0405515",
  "version": "v1",
  "published": "2004-05-27T01:53:36.000Z",
  "updated": "2004-05-27T01:53:36.000Z",
  "title": "Orbits of discrete subgroups on a symmetric space and the Furstenberg boundary",
  "authors": [
    "Alexander Gorodnik",
    "Hee Oh"
  ],
  "categories": [
    "math.DS",
    "math.GR"
  ],
  "abstract": "Let X be a symmetric space of noncompact type and \\Gamma a lattice in the isometry group of X. We study the distribution of orbits of \\Gamma acting on the symmetric space X and its geometric boundary X(\\infty). More precisely, for any y in X and b in X(\\infty), we investigate the distribution of the set {(y\\gamma,b\\gamma^{-1}):\\gamma\\in\\Gamma} in X\\times X(\\infty). It is proved, in particular, that the orbits of \\Gamma in the Furstenberg boundary are equidistributed, and that the orbits of \\Gamma in X are equidistributed in ``sectors'' defined with respect to a Cartan decomposition. We also discuss an application to the Patterson-Sullivan theory. Our main tools are the strong wavefront lemma and the equidistribution of solvable flows on homogeneous spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-05-27T01:53:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57S30",
      "37A17",
      "22E40"
    ],
    "keywords": [
      "symmetric space",
      "furstenberg boundary",
      "discrete subgroups",
      "strong wavefront lemma",
      "distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5515G"
    }
  }
}