{
  "id": "1303.4032",
  "version": "v1",
  "published": "2013-03-17T04:56:39.000Z",
  "updated": "2013-03-17T04:56:39.000Z",
  "title": "Periodic billiard orbits of self-similar Sierpinski carpets",
  "authors": [
    "Joe P. Chen",
    "Robert G. Niemeyer"
  ],
  "comment": "22 Figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We identify a collection of periodic billiard orbits in a self-similar Sierpinski carpet billiard table. Based on a refinement of the result of Durand-Cartagena and Tyson regarding nontrivial line segments in a self-similar Sierpinski carpet, we construct what is called an eventually constant sequence of compatible periodic orbits of prefractal Sierpinski carpet billiard tables. The trivial limit of this sequence then constitutes a periodic orbit of a self-similar Sierpinski carpet billiard table. We also determine the corresponding translation surface for each prefractal billiard table, and show that the genera of a sequence of translation surfaces increase without bound. Various open questions and possible directions for future research are offered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-17T04:56:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic billiard orbits",
      "self-similar sierpinski carpet billiard table",
      "prefractal sierpinski carpet billiard tables",
      "tyson regarding nontrivial line segments"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.4032C"
    }
  }
}