{
  "id": "1108.3441",
  "version": "v3",
  "published": "2011-08-17T10:18:28.000Z",
  "updated": "2013-04-01T10:09:59.000Z",
  "title": "On a Gauss-Kuzmin-Type Problem for a Family of Continued Fraction Expansions",
  "authors": [
    "Dan Lascu"
  ],
  "comment": "This paper has been withdrawn by the author due to a change of the team of authors",
  "journal": "Journal of Number Theory 133 (2013) 2153-2181",
  "doi": "10.1016/j.jnt.2012.12.007",
  "categories": [
    "math.NT",
    "math.PR"
  ],
  "abstract": "In this paper we study in detail a family of continued fraction expansions of any number in the unit closed interval $[0,1]$ whose digits are differences of consecutive non-positive integer powers of an integer $m \\geq 2$. For the transformation which generates this expansion and its invariant measure, the Perron-Frobenius operator is given and studied. For this expansion, we apply the method of random systems with complete connections by Iosifescu and obtained the solution of its Gauss-Kuzmin type problem.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-04-01T10:09:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J70",
      "11K50",
      "28D05",
      "60A10"
    ],
    "keywords": [
      "continued fraction expansions",
      "gauss-kuzmin-type problem",
      "gauss-kuzmin type problem",
      "complete connections",
      "random systems"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.3441L"
    }
  }
}