{
  "id": "0801.0075",
  "version": "v4",
  "published": "2007-12-30T20:51:44.000Z",
  "updated": "2009-02-18T14:14:38.000Z",
  "title": "Non-existence of absolutely continuous invariant probabilities for exponential maps",
  "authors": [
    "Neil Dobbs",
    "Bartlomiej Skorulski"
  ],
  "comment": "4 pages. Similar to the version published in Fundamenta in February 2008",
  "journal": "Fundamenta Mathematicae, 198(3):283-287, 2008",
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that for entire maps of the form $z \\mapsto \\lambda \\exp(z)$ such that the orbit of zero is bounded and such that Lebesgue almost every point is transitive, no absolutely continuous invariant probability measure can exist. This answers a long-standing open problem.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-02-18T14:14:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10"
    ],
    "keywords": [
      "exponential maps",
      "non-existence",
      "absolutely continuous invariant probability measure",
      "entire maps",
      "long-standing open problem"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0801.0075D"
    }
  }
}