{
  "id": "0712.3490",
  "version": "v3",
  "published": "2007-12-20T16:27:01.000Z",
  "updated": "2010-03-02T16:47:18.000Z",
  "title": "Combinatorial rigidity for some infinitely renormalizable unicritical polynomials",
  "authors": [
    "Davoud Cheraghi"
  ],
  "comment": "47 Pages; 7 figures; changes in some proofs; Changes in the writing",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove combinatorial rigidity of infinitely renormalizable unicritical polynomials, P_c :z \\mapsto z^d+c, with complex c, under the a priori bounds and a certain \"combinatorial condition\". This implies the local connectivity of the connectedness loci (the Mandelbrot set when d = 2) at the corresponding parameters.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-03-02T16:47:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F45",
      "37F25",
      "37F30"
    ],
    "keywords": [
      "infinitely renormalizable unicritical polynomials",
      "combinatorial rigidity",
      "mandelbrot set",
      "connectedness loci",
      "priori bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.3490C"
    }
  }
}