{
  "id": "1206.6667",
  "version": "v1",
  "published": "2012-06-28T12:56:18.000Z",
  "updated": "2012-06-28T12:56:18.000Z",
  "title": "On the connectivity of the Julia sets of meromorphic functions",
  "authors": [
    "Krzysztof Baranski",
    "Nuria Fagella",
    "Xavier Jarque",
    "Boguslawa Karpinska"
  ],
  "comment": "34 pages, 10 figures",
  "doi": "10.1007/s00222-014-0504-5",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that every transcendental meromorphic map f with a disconnected Julia set has a weakly repelling fixed point. This implies that the Julia set of Newton's method for finding zeroes of an entire map is connected. Moreover, extending a result of Cowen for holomorphic self-maps of the disc, we show the existence of absorbing domains for holomorphic self-maps of hyperbolic regions whose iterates tend to a boundary point. In particular, the results imply that periodic Baker domains of Newton's method for entire maps are simply connected, which solves a well-known open question.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-06-28T12:56:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "julia set",
      "meromorphic functions",
      "entire map",
      "newtons method",
      "connectivity"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.6667B"
    }
  }
}