{
  "id": "math/0307057",
  "version": "v2",
  "published": "2003-07-03T22:36:22.000Z",
  "updated": "2005-05-17T00:31:19.000Z",
  "title": "A family of critically finite maps with symmetry",
  "authors": [
    "Scott Crass"
  ],
  "comment": "24 pages, 9 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "The symmetric group S_n acts as a reflection group on CP^{n-2} (for $n\\geq 3$) . Associated with each of the $\\binom{n}{2}$ transpositions in S_n is an involution on CP^{n-2} that pointwise fixes a hyperplane--the mirrors of the action. For each such action, there is a unique S_n-symmetric holomorphic map of degree n+1 whose critical set is precisely the collection of hyperplanes. Since the map preserves each reflecting hyperplane, the members of this family are critically-finite in a very strong sense. Considerations of symmetry and critical-finiteness produce global dynamical results: each map's fatou set consists of a special finite set of superattracting points whose basins are dense.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-05-17T00:31:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F45"
    ],
    "keywords": [
      "critically finite maps",
      "critical-finiteness produce global dynamical results",
      "maps fatou set consists",
      "special finite set",
      "reflection group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......7057C"
    }
  }
}