{
  "id": "1706.03882",
  "version": "v1",
  "published": "2017-06-13T01:09:25.000Z",
  "updated": "2017-06-13T01:09:25.000Z",
  "title": "Scarcity of periodic orbits in outer billiards",
  "authors": [
    "Alexander Tumanov"
  ],
  "comment": "12 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We give a simple proof of our previous result with V. Zharnitsky that the set of period 4 orbits in planar outer billiard with piecewise smooth convex boundary has empty interior, provided that no four corners of the boundary form a parallelogram. We also obtain results on period 5 and 6 orbits.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-13T01:09:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D50",
      "37C25"
    ],
    "keywords": [
      "periodic orbits",
      "planar outer billiard",
      "piecewise smooth convex boundary",
      "simple proof",
      "boundary form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}