{
  "id": "1108.5574",
  "version": "v2",
  "published": "2011-08-29T14:36:32.000Z",
  "updated": "2014-06-26T18:20:58.000Z",
  "title": "Substitutive Arnoux-Rauzy sequences have pure discrete spectrum",
  "authors": [
    "Valérie Berthé",
    "Timo Jolivet",
    "Anne Siegel"
  ],
  "comment": "19 pages, v2 includes some corrections to match the published version, and a mistake in the graph of Fig. 1 has been corrected",
  "journal": "Uniform Distribution Theory 7 (2012), no. 1, 173-197",
  "categories": [
    "math.DS",
    "cs.DM",
    "math.CO"
  ],
  "abstract": "We prove that the symbolic dynamical system generated by a purely substitutive Arnoux-Rauzy sequence is measurably conjugate to a toral translation. The proof is based on an explicit construction of a fundamental domain with fractal boundary (a Rauzy fractal) for this toral translation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-06-26T18:20:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "pure discrete spectrum",
      "toral translation",
      "rauzy fractal",
      "purely substitutive arnoux-rauzy sequence",
      "explicit construction"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.5574B"
    }
  }
}