{
  "id": "0711.2672",
  "version": "v1",
  "published": "2007-11-16T20:16:54.000Z",
  "updated": "2007-11-16T20:16:54.000Z",
  "title": "Hyperbolic dimension of Julia sets of meromorphic maps with logarithmic tracts",
  "authors": [
    "Krzysztof Barański",
    "Bogusława Karpińska",
    "Anna Zdunik"
  ],
  "comment": "7 pages, 1 figure",
  "journal": "Internat. Math. Res. Notices 2009 (2009), 615-624",
  "doi": "10.1093/imrn/rnn141",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that for meromorphic maps with logarithmic tracts (e.g. entire or meromorphic maps with a finite number of poles from class $\\mathcal B$), the Julia set contains a compact invariant hyperbolic Cantor set of Hausdorff dimension greater than 1. Hence, the hyperbolic dimension of the Julia set is greater than 1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-16T20:16:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "37F35",
      "30D40",
      "28A80"
    ],
    "keywords": [
      "meromorphic maps",
      "hyperbolic dimension",
      "logarithmic tracts",
      "compact invariant hyperbolic cantor set",
      "julia set contains"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.2672B"
    }
  }
}