{
  "id": "math/0507240",
  "version": "v1",
  "published": "2005-07-12T18:21:22.000Z",
  "updated": "2005-07-12T18:21:22.000Z",
  "title": "Combinatorial rigidity for unicritical polynomials",
  "authors": [
    "Artur Avila",
    "Jeremy Kahn",
    "Mikhail Lyubich",
    "Weixiao Shen"
  ],
  "comment": "LaTeX, 12 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that any unicritical polynomial $f_c:z\\mapsto z^d+c$ which is at most finitely renormalizable and has only repelling periodic points is combinatorially rigid. It implies that the connectedness locus (the ``Multibrot set'') is locally connected at the corresponding parameter values. It generalizes Yoccoz's Theorem for quadratics to the higher degree case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-07-12T18:21:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F45"
    ],
    "keywords": [
      "unicritical polynomial",
      "combinatorial rigidity",
      "generalizes yoccozs theorem",
      "higher degree case",
      "repelling periodic points"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......7240A"
    }
  }
}