{
  "id": "0901.3014",
  "version": "v1",
  "published": "2009-01-20T10:12:36.000Z",
  "updated": "2009-01-20T10:12:36.000Z",
  "title": "On the Hausdorff dimension of the escaping set of certain meromorphic functions",
  "authors": [
    "Walter Bergweiler",
    "Janina Kotus"
  ],
  "comment": "23 pages",
  "journal": "Trans. Amer. Math. Soc. 364 (2012), 5369-5394",
  "doi": "10.1090/S0002-9947-2012-05514-0",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "The escaping set I(f) of a transcendental meromorphic function f consists of all points which tend to infinity under iteration. The Eremenko-Lyubich class B consists of all transcendental meromorphic functions for which the set of finite critical and asymptotic values of f is bounded. It is shown that if f is in B and of finite order of growth, if infinity is not an asymptotic value of f and if the multiplicities of the poles of f are uniformly bounded, then the Hausdorff dimension of I(f) is strictly smaller than 2. In fact, we give a sharp bound for the Hausdorff dimension of I(f) in terms of the order of f and the bound for the multiplicities of the poles. If f satisfies the above hypotheses but is of infinite order, then the area of I(f) is zero. This result does not hold without a restriction on the multiplicities of the poles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-01-20T10:12:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "30D05",
      "30D15"
    ],
    "keywords": [
      "hausdorff dimension",
      "escaping set",
      "transcendental meromorphic function",
      "asymptotic value",
      "multiplicities"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Trans. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0901.3014B"
    }
  }
}