{
  "id": "0904.3072",
  "version": "v1",
  "published": "2009-04-20T16:34:38.000Z",
  "updated": "2009-04-20T16:34:38.000Z",
  "title": "Hausdorff dimensions of escaping sets of transcendental entire functions",
  "authors": [
    "Lasse Rempe",
    "Gwyneth M. Stallard"
  ],
  "comment": "9 pages",
  "journal": "Proc. Amer. Math. Soc. 138 (2010), 1657-1665.",
  "doi": "10.1090/S0002-9939-09-10104-1",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "Let $f$ and $g$ be transcendental entire functions, each with a bounded set of singular values, and suppose that $f$ and $g$ are affinely equivalent (that is, $g \\circ \\phi= \\psi\\circ f$, where $\\phi,\\psi:\\C\\to\\C$ are affine). We show that the escaping sets of $f$ and $g$ have the same Hausdorff dimension. Using a result of the second author, we deduce that there exists a family of transcendental entire functions for which the escaping set has Hausdorff dimension equal to one.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-20T16:34:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "37F35",
      "30D05"
    ],
    "keywords": [
      "transcendental entire functions",
      "escaping set",
      "hausdorff dimension equal",
      "second author",
      "singular values"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Proc. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.3072R"
    }
  }
}