{
  "id": "1305.5799",
  "version": "v2",
  "published": "2013-05-24T17:03:21.000Z",
  "updated": "2014-11-10T18:43:41.000Z",
  "title": "Quadratic-like dynamics of cubic polynomials",
  "authors": [
    "Alexander Blokh",
    "Lex Oversteegen",
    "Ross Ptacek",
    "Vladlen Timorin"
  ],
  "comment": "21 pages. In the new version we strengthen some of the results using new arguments. A preprint \"Complementary components to the cubic Principal Hyperbolic Domain\" with related results is being posted to arxiv too",
  "categories": [
    "math.DS"
  ],
  "abstract": "A small perturbation of a quadratic polynomial with a non-repelling fixed point gives a polynomial with an attracting fixed point and a Jordan curve Julia set, on which the perturbed polynomial acts like angle doubling. However, there are cubic polynomials with a non-repelling fixed point, for which no perturbation results into a polynomial with Jordan curve Julia set. Motivated by the study of the closure of the Cubic Principal Hyperbolic Domain, we describe such polynomials in terms of their quadratic-like restrictions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-24T17:03:21.000Z",
      "comment": "34 pages, 1 figure",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-11-10T18:43:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F45",
      "37F10",
      "37F20",
      "37F50"
    ],
    "keywords": [
      "cubic polynomials",
      "jordan curve julia set",
      "quadratic-like dynamics",
      "cubic principal hyperbolic domain",
      "non-repelling fixed point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.5799B"
    }
  }
}