{
  "id": "math/0406256",
  "version": "v1",
  "published": "2004-06-13T22:24:28.000Z",
  "updated": "2004-06-13T22:24:28.000Z",
  "title": "Hyperbolic Components in Exponential Parameter Space",
  "authors": [
    "Dierk Schleicher"
  ],
  "comment": "To appear in: Comptes Rendues Acad Sci Paris.-- Detailed description of results can be found in ArXiv math.DS/0311480.-- 6 pages, 1 figure",
  "journal": "Comptes Rendus Mathematiques 339/3 (2004) 223-228",
  "doi": "10.1016/j.crma.2004.05.014",
  "categories": [
    "math.DS"
  ],
  "abstract": "We discuss the space of complex exponential maps $\\Ek\\colon z\\mapsto e^{z}+\\kappa$. We prove that every hyperbolic component $W$ has connected boundary, and there is a conformal isomorphism $\\Phi_W\\colon W\\to\\half^-$ which extends to a homeomorphism of pairs $\\Phi_W\\colon(\\ovl W,W)\\to(\\ovl\\half^-,\\half^-)$. This solves a conjecture of Baker and Rippon, and of Eremenko and Lyubich, in the affirmative. We also prove a second conjecture of Eremenko and Lyubich.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-06-13T22:24:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30D05",
      "37F10",
      "37F15",
      "37F20",
      "37F45"
    ],
    "keywords": [
      "exponential parameter space",
      "hyperbolic component",
      "complex exponential maps",
      "second conjecture",
      "conformal isomorphism"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......6256S"
    }
  }
}