{
  "id": "math/0505194",
  "version": "v1",
  "published": "2005-05-10T17:51:57.000Z",
  "updated": "2005-05-10T17:51:57.000Z",
  "title": "Local connectivity of Julia sets for unicritical polynomials",
  "authors": [
    "Jeremy Kahn",
    "Mikhail Lyubich"
  ],
  "comment": "LaTeX, 14 pages, 1 figure",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that the Julia set $J(f)$ of at most finitely renormalizable unicritical polynomial $f:z\\mapsto z^d+c$ with all periodic points repelling is locally connected. (For $d=2$ it was proved by Yoccoz around 1990.) It follows from a priori bounds in a modified Principle Nest of puzzle pieces. The proof of a priori bounds makes use of new analytic tools developed in math.DS/0505191 that give control of moduli of annuli under maps of high degree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-05-10T17:51:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F45"
    ],
    "keywords": [
      "julia set",
      "local connectivity",
      "priori bounds",
      "high degree",
      "puzzle pieces"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......5194K"
    }
  }
}