{
  "id": "1603.03527",
  "version": "v1",
  "published": "2016-03-11T05:38:16.000Z",
  "updated": "2016-03-11T05:38:16.000Z",
  "title": "Rotation Sets of Billiards with N Obstacles on a Torus",
  "authors": [
    "Zainab Alsheekhhussain"
  ],
  "comment": "12 pAGES, Rotation sets of billiards with N obstacles on a torus, Differ. Equ. Dyn. Syst. (2015)",
  "doi": "10.1007/s12591-015-0269-3",
  "categories": [
    "math.DS"
  ],
  "abstract": "For billiards with $N$ obstacles on a torus, we study the behavior of specific kind of its trajectories, \\emph{the so called admissible trajectories}. Using the methods developed in \\cite{1}, we prove that the \\emph{admissible rotation set} is convex, and the periodic trajectories of admissible type are dense in the admissible rotation set. In addition, we show that the admissible rotation set is a proper subset of the general rotation set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-11T05:38:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "admissible rotation set",
      "general rotation set",
      "specific kind",
      "periodic trajectories",
      "proper subset"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160303527A"
    }
  }
}