{
  "id": "1009.0468",
  "version": "v1",
  "published": "2010-09-02T16:37:02.000Z",
  "updated": "2010-09-02T16:37:02.000Z",
  "title": "Geometric renormalisation and Hausdorff dimension for loop-approximable geodesics escaping to infinity",
  "authors": [
    "Kurt Falk",
    "Bernd O. Stratmann"
  ],
  "comment": "11 pages, 3 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "The main result of this paper is to show that if $\\H$ is a normal subgroup of a Kleinian group $G$ such that $G/\\H$ contains a coset which is represented by some loxodromic element, then the Hausdorff dimension of the transient limit set of $\\H$ coincides with the Hausdorff dimension of the limit set of $G$. This observation extends previous results by Fern\\'andez and Meli\\'an for Riemann surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-09-02T16:37:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hausdorff dimension",
      "loop-approximable geodesics escaping",
      "geometric renormalisation",
      "transient limit set",
      "riemann surfaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.0468F"
    }
  }
}