{
  "id": "0902.1065",
  "version": "v1",
  "published": "2009-02-06T11:18:15.000Z",
  "updated": "2009-02-06T11:18:15.000Z",
  "title": "Dimension properties of the boundaries of exponential basins",
  "authors": [
    "Krzysztof Barański",
    "Bogusława Karpińska",
    "Anna Zdunik"
  ],
  "comment": "13 pages, 1 figure",
  "journal": "Bull. Lond. Math. Soc. 42 (2010), 210-220",
  "doi": "10.1112/blms/bdp105",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that the boundary of a component $U$ of the basin of an attracting periodic cycle (of period greater than 1) for an exponential map on the complex plane has Hausdorff dimension greater than 1 and less than 2. Moreover, the set of points in the boundary of $U$ which do not escape to infinity has Hausdorff dimension (in fact: hyperbolic dimension) greater than 1, while the set of points in the boundary of $U$ which escape to infinity has Hausdorff dimension 1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-06T11:18:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "37F35",
      "30D40",
      "28A80"
    ],
    "keywords": [
      "dimension properties",
      "exponential basins",
      "hausdorff dimension greater",
      "period greater",
      "hyperbolic dimension"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.1065B"
    }
  }
}