{
  "id": "1701.08825",
  "version": "v1",
  "published": "2017-01-30T21:00:02.000Z",
  "updated": "2017-01-30T21:00:02.000Z",
  "title": "Models for spaces of dendritic polynomials",
  "authors": [
    "Alexander Blokh",
    "Lex Oversteegen",
    "Ross Ptacek",
    "Vladlen Timorin"
  ],
  "comment": "23 pages, 1 figure",
  "categories": [
    "math.DS"
  ],
  "abstract": "Complex 1-variable polynomials with connected Julia sets and only repelling periodic points are called \\emph{dendritic}. By results of Kiwi, any dendritic polynomial is semi-conjugate to a topological polynomial whose topological Julia set is a dendrite. We construct a continuous map of the space of all cubic dendritic polynomials onto a laminational model that is a quotient space of a subset of the closed bidisk. This construction generalizes the \"pinched disk\" model of the Mandelbrot set due to Douady and Thurston. It can be viewed as a step towards constructing a model of the cubic connectedness locus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-30T21:00:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F20",
      "37F10",
      "37F50"
    ],
    "keywords": [
      "cubic connectedness locus",
      "cubic dendritic polynomials",
      "mandelbrot set",
      "construction generalizes",
      "quotient space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}