{
  "id": "0802.0666",
  "version": "v3",
  "published": "2008-02-05T16:54:48.000Z",
  "updated": "2010-08-06T15:43:53.000Z",
  "title": "Absence of line fields and Mane's theorem for non-recurrent transcendental functions",
  "authors": [
    "Lasse Rempe",
    "Sebastian van Strien"
  ],
  "comment": "28 pages; V3. Proof of Theorem 7.4 corrected, as well as some other minor corrections",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "Let f be a transcendental meromorphic function. Suppose that the finite part of the postsingular set of f is bounded, that f has no recurrent critical points or wandering domains, and that the degree of pre-poles of f is uniformly bounded. Then we show that f supports no invariant line fields on its Julia set. We prove this by generalizing two results about rational functions to the transcendental setting: a theorem of Mane about the branching of iterated preimages of disks, and a theorem of McMullen regarding absence of invariant line fields for \"measurably transitive\" functions. Both our theorems extend results previously obtained by Graczyk, Kotus and Swiatek.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-08-06T15:43:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "30D05",
      "37D25",
      "27F15",
      "37F35"
    ],
    "keywords": [
      "non-recurrent transcendental functions",
      "manes theorem",
      "invariant line fields",
      "theorems extend results",
      "transcendental meromorphic function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0802.0666R"
    }
  }
}