{
  "id": "1611.09281",
  "version": "v1",
  "published": "2016-11-28T18:46:40.000Z",
  "updated": "2016-11-28T18:46:40.000Z",
  "title": "Irreducibility of the set of cubic polynomials with one periodic critical point",
  "authors": [
    "Matthieu Arfeux",
    "Jan Kiwi"
  ],
  "comment": "17 pages, 4 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "The space of monic centered cubic polynomials with marked critical points is isomorphic to C^2. For each n>0, the locus Sn formed by all polynomials with a specified critical point periodic of exact period n forms an affine algebraic set. We prove that Sn is irreducible, thus giving an affirmative answer to a question posed by Milnor.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-28T18:46:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "37F20",
      "37F30",
      "14H10"
    ],
    "keywords": [
      "periodic critical point",
      "irreducibility",
      "monic centered cubic polynomials",
      "affine algebraic set",
      "locus sn"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}