{
  "id": "1302.6121",
  "version": "v2",
  "published": "2013-02-25T15:25:34.000Z",
  "updated": "2013-05-22T00:28:18.000Z",
  "title": "Continued fractions on the Heisenberg group",
  "authors": [
    "Anton Lukyanenko",
    "Joseph Vandehey"
  ],
  "comment": "Version 2 introduces significant changes to the text, especially Section 4 on the dynamical properties of the Heisenberg Gauss map",
  "categories": [
    "math.NT",
    "math.DS",
    "math.GR",
    "math.MG"
  ],
  "abstract": "We provide a generalization of continued fractions to the Heisenberg group. We prove an explicit estimate on the rate of convergence of the infinite continued fraction and several surprising analogs of classical formulas about continued fractions. We then discuss dynamical properties of the associated Gauss map, comparing them with base-$b$ expansions on the Heisenberg group and continued fractions on the complex plane.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-05-22T00:28:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E40",
      "11J70",
      "53C17"
    ],
    "keywords": [
      "heisenberg group",
      "infinite continued fraction",
      "explicit estimate",
      "associated gauss map",
      "complex plane"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.6121L"
    }
  }
}