{
  "id": "1205.5340",
  "version": "v1",
  "published": "2012-05-24T06:18:54.000Z",
  "updated": "2012-05-24T06:18:54.000Z",
  "title": "Homotopical rigidity of polygonal billiards",
  "authors": [
    "Jozef Bobok",
    "Serge Troubetzkoy"
  ],
  "journal": "Topology and its Applications (2014) 308-324",
  "doi": "10.1016/j.topol.2014.06.003",
  "categories": [
    "math.DS"
  ],
  "abstract": "Consider two $k$-gons $P$ and $Q$. We say that the billiard flows in $P$ and $Q$ are homotopically equivalent if the set of conjugacy classes in the fundamental group of $P$ which contain a periodic billiard orbit agrees with the analogous set for $Q$. We study this equivalence relationship and compare it to the equivalence relations, order equivalence and code equivalence, introduced in \\cite{BT1,BT2}. In particular we show if $P$ is a rational polygon, and $Q$ is homotopically equivalent to $P$, then $P$ and $Q$ are similar, or affinely similar if all sides of $P$ are vertical and horizontal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-24T06:18:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "polygonal billiards",
      "homotopical rigidity",
      "periodic billiard orbit agrees",
      "homotopically equivalent",
      "code equivalence"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.5340B"
    }
  }
}