{
  "id": "2005.00380",
  "version": "v1",
  "published": "2020-05-01T13:56:41.000Z",
  "updated": "2020-05-01T13:56:41.000Z",
  "title": "Comparison of various continued fraction expansions: a Lochs-type approach",
  "authors": [
    "Dan Lascu",
    "Gabriela Ileana Sebe"
  ],
  "comment": "15 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We investigate the efficiency of several types of continued fraction expansions of a number in the unit interval using a generalization of Loch's theorem from 1964. Thus, we aimed to compare the effectiveness of Chan's continued fractions, $\\theta-$expansions, $N-$continued fractions and R\\'enyi-type continued fractions. A central role in fulfilling our goal is the entropy of the measure preserving transformations which generate these expansions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-01T13:56:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J70",
      "37A35"
    ],
    "keywords": [
      "continued fraction expansions",
      "lochs-type approach",
      "comparison",
      "measure preserving transformations",
      "central role"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}