{
  "id": "1709.08035",
  "version": "v1",
  "published": "2017-09-23T10:58:40.000Z",
  "updated": "2017-09-23T10:58:40.000Z",
  "title": "On the density of intermediate β-shifts of finite type",
  "authors": [
    "Bing Li",
    "Tuomas Sahlsten",
    "Tony Samuel",
    "Wolfgang Steiner"
  ],
  "comment": "6 pages",
  "categories": [
    "math.DS",
    "math.NT"
  ],
  "abstract": "We determine the structure of the set of intermediate $\\beta$-shifts of finite type. Specifically, we show that this set is dense in the parameter space $\\Delta = \\{ (\\beta, \\alpha) \\in \\mathbb{R}^{2} \\colon \\beta \\in (1, 2) \\; \\text{and} \\; 0 \\leq \\alpha \\leq 2 - \\beta\\}$. This generalises the classical result of Parry from 1960 for greedy and (normalised) lazy $\\beta$-shifts.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-23T10:58:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E05",
      "37B10",
      "11A67",
      "11R06"
    ],
    "keywords": [
      "finite type",
      "intermediate",
      "parameter space",
      "generalises"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}