{
  "id": "1012.2131",
  "version": "v3",
  "published": "2010-12-09T21:34:16.000Z",
  "updated": "2012-05-30T21:40:41.000Z",
  "title": "Dynamics of continued fractions and kneading sequences of unimodal maps",
  "authors": [
    "Claudio Bonanno",
    "Carlo Carminati",
    "Stefano Isola",
    "Giulio Tiozzo"
  ],
  "comment": "21 pages, 3 figures. New section added with additional results and applications. Figures and references added. Introduction rearranged",
  "journal": "Discrete and Continuous Dynamical Systems 33, no.4 (2013), pp. 1313-1332",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper we construct a correspondence between the parameter spaces of two families of one-dimensional dynamical systems, the alpha-continued fraction transformations T_alpha and unimodal maps. This correspondence identifies bifurcation parameters in the two families, and allows one to transfer topological and metric properties from one setting to the other. As an application, we recover results about the real slice of the Mandelbrot set, and the set of univoque numbers.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-05-30T21:40:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A55",
      "37A10",
      "37E05",
      "37E20",
      "11J06"
    ],
    "keywords": [
      "unimodal maps",
      "kneading sequences",
      "continued fractions",
      "correspondence identifies bifurcation parameters",
      "one-dimensional dynamical systems"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.2131B"
    }
  }
}