{
  "id": "1404.5698",
  "version": "v3",
  "published": "2014-04-23T04:08:25.000Z",
  "updated": "2015-03-08T02:09:16.000Z",
  "title": "Closed geodesics and holonomies for Kleinian manifolds",
  "authors": [
    "Gregory Margulis",
    "Amir Mohammadi",
    "Hee Oh"
  ],
  "comment": "27 pages, Minor corrections in the main term of the effective versions of Theorem 1.2, 1.3 and 5.1 are made from the printed version (GAFA,Vol 24 (2014) 1608-1636)",
  "categories": [
    "math.DS"
  ],
  "abstract": "For a rank one Lie group G and a Zariski dense and geometrically finite subgroup $\\Gamma$ of G, we establish equidistribution of holonomy classes about closed geodesics for the associated locally symmetric space. Our result is given in a quantitative form for real hyperbolic geometrically finite manifolds whose critical exponents are big enough. In the case when G=PSL(2, C), our results can be interpreted as the equidistribution of eigenvalues of $\\Gamma$ in the complex plane. When $\\Gamma$ is a lattice, this result was proved by Sarnak and Wakayama in 1999.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-04T06:12:31.000Z",
      "comment": "27 pages, several minor revisions made. To appear in GAFA",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-03-08T02:09:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "closed geodesics",
      "kleinian manifolds",
      "real hyperbolic geometrically finite manifolds",
      "geometrically finite subgroup",
      "symmetric space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.5698M"
    }
  }
}