{
  "id": "1311.7277",
  "version": "v2",
  "published": "2013-11-28T11:28:15.000Z",
  "updated": "2014-01-26T15:12:19.000Z",
  "title": "Equivalence classes of codimension one cut-and-project nets",
  "authors": [
    "Alan Haynes"
  ],
  "comment": "19 pages, added some references and sharpened statements of some of the results",
  "categories": [
    "math.DS",
    "math.NT"
  ],
  "abstract": "We prove that in any totally irrational cut-and-project setup with codimension (internal space dimension) one, it is possible to choose sections (windows) in non-trivial ways so that the resulting sets are bounded displacement to lattices. Our proof demonstrates that for any irrational $\\alpha$, regardless of Diophantine type, there is a collection of intervals in $\\mathbb{R}/\\mathbb{Z}$ which is closed under translation, contains intervals of arbitrarily small length, and along which the discrepancy of the sequence $\\{n\\alpha\\}$ is bounded above uniformly by a constant.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-01-26T15:12:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cut-and-project nets",
      "equivalence classes",
      "codimension",
      "totally irrational cut-and-project setup",
      "internal space dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.7277H"
    }
  }
}