{
  "id": "1506.00067",
  "version": "v1",
  "published": "2015-05-30T03:42:34.000Z",
  "updated": "2015-05-30T03:42:34.000Z",
  "title": "Topological dynamics of the doubling map with asymmetrical holes",
  "authors": [
    "Rafael Alcaraz Barrera"
  ],
  "comment": "33 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the dynamics of the attractor of the doubling map with an asymmetrical hole by associating to each hole an element of the lexicographic world. A description of the topological entropy function is given. We show that the set of parameters $(a,b)$ such that the dynamics of the mentioned attractor corresponds to a subshift of finite type is open and dense. Using the connections between this family of open dynamical systems, intermediate $\\beta$-expansions and Lorenz maps we study the topological transitivity and the specification property for such maps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-30T03:42:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10",
      "37C70",
      "37E05",
      "68R15"
    ],
    "keywords": [
      "doubling map",
      "asymmetrical hole",
      "topological dynamics",
      "topological entropy function",
      "specification property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150600067A"
    }
  }
}