{
  "id": "0902.2686",
  "version": "v1",
  "published": "2009-02-16T14:00:34.000Z",
  "updated": "2009-02-16T14:00:34.000Z",
  "title": "Karpińska's paradox in dimension three",
  "authors": [
    "Walter Bergweiler"
  ],
  "comment": "21 pages",
  "journal": "Duke Math. J. 154 (2010), 599-630",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "For 0 < c < 1/e the Julia set of f(z) = c exp(z) is an uncountable union of pairwise disjoint simple curves tending to infinity [Devaney and Krych 1984], the Hausdorff dimension of this set is two [McMullen 1987], but the set of curves without endpoints has Hausdorff dimension one [Karpinska 1999]. We show that these results have three-dimensional analogues when the exponential function is replaced by a quasiregular self-map of three-space introduced by Zorich.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-16T14:00:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F35",
      "30C65",
      "30D10",
      "37F10"
    ],
    "keywords": [
      "karpińskas paradox",
      "hausdorff dimension",
      "pairwise disjoint simple curves tending",
      "julia set",
      "three-dimensional analogues"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.2686B"
    }
  }
}