{
  "id": "math/9408217",
  "version": "v1",
  "published": "1994-08-26T00:00:00.000Z",
  "updated": "1994-08-26T00:00:00.000Z",
  "title": "Some remarks on periodic billiard orbits in rational polygons",
  "authors": [
    "Michael Boshernitzan",
    "G. A. Galperin",
    "Tyll Krüger",
    "Serge Troubetzkoy"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "A polygon is called rational if the angle between each pair of sides is a rational multiple of $\\pi.$ The main theorem we will prove is Theorem 1: For rational polygons, periodic points of the billiard flow are dense in the phase space of the billiard flow. This is a strengthening of Masur's theorem, who has shown that any rational polygon has ``many'' periodic billiard trajectories; more precisely, the set of directions of the periodic trajectories are dense in the set of velocity directions $\\S^1.$ We will also prove some refinements of Theorem 1: the ``well distribution'' of periodic orbits in the polygon and the residuality of the points $q \\in Q$ with a dense set of periodic directions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1994-08-26T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic billiard orbits",
      "rational polygon",
      "billiard flow",
      "periodic billiard trajectories",
      "main theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1994math......8217B"
    }
  }
}