{
  "id": "1108.0987",
  "version": "v2",
  "published": "2011-08-04T02:57:45.000Z",
  "updated": "2011-10-28T23:10:45.000Z",
  "title": "Three-Period Orbits in Billiards on the Surfaces of Constant Curvature",
  "authors": [
    "Victoria Blumen",
    "Ki Yeun Kim",
    "Joe Nance",
    "Vadim Zharnitsky"
  ],
  "comment": "10 pages, 3 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "An approach due to Wojtkovski [9], based on the Jacobi fields, is applied to study sets of 3-period orbits in billiards on hyperbolic plane and on two-dimensional sphere. It is found that the set of 3-period orbits in billiards on hyperbolic plane, as in the planar case, has zero measure. For the sphere, a new proof of Baryshnikov's theorem is obtained which states that 3-period orbits can form a set of positive measure provided a natural condition on the orbit length is satisfied.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-10-28T23:10:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "constant curvature",
      "three-period orbits",
      "hyperbolic plane",
      "zero measure",
      "jacobi fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.0987B"
    }
  }
}