{
  "id": "1205.5093",
  "version": "v1",
  "published": "2012-05-23T05:08:56.000Z",
  "updated": "2012-05-23T05:08:56.000Z",
  "title": "Classification of rotations on the torus $\\mathbb{T}^2$",
  "authors": [
    "Nicolas Bédaride"
  ],
  "comment": "18 pages, 4 figures",
  "journal": "Theoretical Computer science. 2007, volume 385, issues 1-3, pages 214-225",
  "categories": [
    "math.DS",
    "math.CO"
  ],
  "abstract": "We consider rotations on the torus $\\mathbb{T}^2$, and we classify them with respect to the complexity functions. In dimension one, a minimal rotation can be coded by a sturmian word. A sturmian word has complexity $n+1$ by the Morse-Hedlund theorem. Here we make a generalization in dimension two.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-23T05:08:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "classification",
      "sturmian word",
      "complexity functions",
      "minimal rotation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.5093B"
    }
  }
}