{
  "id": "1708.02819",
  "version": "v1",
  "published": "2017-08-09T13:01:46.000Z",
  "updated": "2017-08-09T13:01:46.000Z",
  "title": "Lebesgue measure of Julia sets and escaping sets of certain entire functions",
  "authors": [
    "Walter Bergweiler"
  ],
  "comment": "26 pages, 1 figure",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "We give criteria for the escaping set and the Julia set of an entire function to have positive measure. The results are applied to Poincar\\'e functions of semihyperbolic polynomials and to the Weierstra{\\ss} $\\sigma$-function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-09T13:01:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "30D05"
    ],
    "keywords": [
      "julia set",
      "entire function",
      "escaping set",
      "lebesgue measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}