{
  "id": "1211.3019",
  "version": "v1",
  "published": "2012-11-13T15:23:00.000Z",
  "updated": "2012-11-13T15:23:00.000Z",
  "title": "Amount of failure of upper-semicontinuity of entropy in noncompact rank one situations, and Hausdorff dimension",
  "authors": [
    "Shirali Kadyrov",
    "Anke D. Pohl"
  ],
  "comment": "24 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Recently, Einsiedler and the authors provided a bound in terms of escape of mass for the amount by which upper-semicontinuity for metric entropy fails for diagonal flows on homogeneous spaces $\\Gamma\\backslash G$, where $G$ is any connected semisimple Lie group of real rank 1 with finite center and $\\Gamma$ is any nonuniform lattice in $G$. We show that this bound is sharp and apply the methods used to establish bounds for the Hausdorff dimension of the set of points which diverge on average.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-13T15:23:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A35",
      "37D40",
      "28D20",
      "22D40"
    ],
    "keywords": [
      "hausdorff dimension",
      "noncompact rank",
      "upper-semicontinuity",
      "situations",
      "metric entropy fails"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.3019K"
    }
  }
}