{
  "id": "1104.1051",
  "version": "v1",
  "published": "2011-04-06T10:20:40.000Z",
  "updated": "2011-04-06T10:20:40.000Z",
  "title": "Periodic billiard trajectories in polyhedra",
  "authors": [
    "Nicolas Bedaride"
  ],
  "comment": "15 pages, 3 figures",
  "journal": "Forum geometricorum Volume 8 (2008), pages 107-120",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider the billiard map inside a polyhedron. We give a condition for the stability of the periodic trajectories. We apply this result to the case of the tetrahedron. We deduce the existence of an open set of tetrahedra which have a periodic orbit of length four (generalization of Fagnano's orbit for triangles), moreover we can study completly the orbit of points along this coding.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-06T10:20:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic billiard trajectories",
      "polyhedron",
      "billiard map inside",
      "periodic trajectories",
      "tetrahedron"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.1051B"
    }
  }
}