{
  "id": "math/0604388",
  "version": "v1",
  "published": "2006-04-18T09:32:53.000Z",
  "updated": "2006-04-18T09:32:53.000Z",
  "title": "On configuration spaces of plane polygons, sub-Riemannian geometry and periodic orbits of outer billiards",
  "authors": [
    "D. Genin",
    "S. Tabachnikov"
  ],
  "categories": [
    "math.DG",
    "math.DS"
  ],
  "abstract": "Following a recent paper by Baryshnikov and Zharnitskii, we consider outer billiards in the plane possessing invariant curves consisting of periodic orbits. We prove the existence and abundance of such tables using tools from sub-Riemannian geometry. We also prove that the set of 3-periodic outer billiard orbits has zero measure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-04-18T09:32:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic orbits",
      "sub-riemannian geometry",
      "plane polygons",
      "configuration spaces",
      "possessing invariant curves consisting"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......4388G"
    }
  }
}