{
  "id": "1109.6410",
  "version": "v1",
  "published": "2011-09-29T06:23:00.000Z",
  "updated": "2011-09-29T06:23:00.000Z",
  "title": "Billiard complexity in the hypercube",
  "authors": [
    "Nicolas Bedaride",
    "Pascal Hubert"
  ],
  "comment": "18 pages, 3 figures",
  "journal": "Annales de l'institut Fourier. 2007, 57 (3) 719-738",
  "categories": [
    "math.DS",
    "math.CO"
  ],
  "abstract": "We consider the billiard map in the hypercube of $\\mathbb{R}^d$. We obtain a language by coding the billiard map by the faces of the hypercube. We investigate the complexity function of this language. We prove that $n^{3d-3}$ is the order of magnitude of the complexity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-09-29T06:23:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A35",
      "37C35",
      "05A16",
      "11N37"
    ],
    "keywords": [
      "billiard complexity",
      "billiard map",
      "complexity function"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.6410B"
    }
  }
}