{
  "id": "math/0605058",
  "version": "v3",
  "published": "2006-05-02T14:17:03.000Z",
  "updated": "2009-01-21T13:52:33.000Z",
  "title": "Rigidity of escaping dynamics for transcendental entire functions",
  "authors": [
    "Lasse Rempe"
  ],
  "comment": "28 pages; 2 figures. Final version (October 2008). Various modificiations were made, including the introduction of Proposition 3.6, which was not formally stated previously, and the inclusion of a new figure. No major changes otherwise",
  "journal": "Acta Mathematica 203 (2009), no 2, 235 --267",
  "doi": "10.1007/s11511-009-0042-y",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "We prove an analog of Boettcher's theorem for transcendental entire functions in the Eremenko-Lyubich class B. More precisely, let f and g be entire functions with bounded sets of singular values and suppose that f and g belong to the same parameter space (i.e., are *quasiconformally equivalent* in the sense of Eremenko and Lyubich). Then f and g are conjugate when restricted to the set of points which remain in some sufficiently small neighborhood of infinity under iteration. Furthermore, this conjugacy extends to a quasiconformal self-map of the plane. We also prove that this conjugacy is essentially unique. In particular, we show that an Eremenko-Lyubich class function f has no invariant line fields on its escaping set. Finally, we show that any two hyperbolic Eremenko-Lyubich class functions f and g which belong to the same parameter space are conjugate on their sets of escaping points.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-01-21T13:52:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "30D05"
    ],
    "keywords": [
      "transcendental entire functions",
      "escaping dynamics",
      "hyperbolic eremenko-lyubich class functions",
      "parameter space",
      "invariant line fields"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......5058R"
    }
  }
}