{
  "id": "0810.2260",
  "version": "v1",
  "published": "2008-10-13T16:15:31.000Z",
  "updated": "2008-10-13T16:15:31.000Z",
  "title": "Rational functions with real multipliers",
  "authors": [
    "Alexandre Eremenko",
    "Sebastian van Strien"
  ],
  "comment": "16 pages 1 figure",
  "journal": "Trans. AMS, 363, 12 (2011) 6453-6463",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "Let f be a rational function such that the multipliers of all repelling periodic points are real. We prove that the Julia set of such a function belongs to a circle. Combining this with a result of Fatou we conclude that whenever J(f) belongs to a smooth curve, it also belongs to a circle. Then we discuss rational functions whose Julia sets belong to a circle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-13T16:15:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "30D05"
    ],
    "keywords": [
      "rational function",
      "real multipliers",
      "julia sets belong",
      "repelling periodic points",
      "function belongs"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Trans. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.2260E"
    }
  }
}