{
  "id": "1902.08387",
  "version": "v1",
  "published": "2019-02-22T07:55:18.000Z",
  "updated": "2019-02-22T07:55:18.000Z",
  "title": "Complexity and invariant measure of the period-doubling subshift",
  "authors": [
    "Miroslava Poláková"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Explicit formulas for complexity and unique invariant measure of the period-doubling subshift can be derived from those for the Thue-Morse subshift, obtained by Brlek, De Luca and Varricchio, and Dekking. In this note we give direct proofs based on combinatorial properties of the period-doubling sequence. We also derive explicit formulas for correlation integral and other recurrence characteristics of the period-doubling subshift. As a corollary we obtain that the determinism of this subshift converges to 1 as the distance threshold approaches 0.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-22T07:55:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10",
      "37A35",
      "68R15"
    ],
    "keywords": [
      "period-doubling subshift",
      "complexity",
      "unique invariant measure",
      "distance threshold approaches",
      "direct proofs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}