{
  "id": "1505.07902",
  "version": "v1",
  "published": "2015-05-29T01:35:22.000Z",
  "updated": "2015-05-29T01:35:22.000Z",
  "title": "Rotation Sets of Open Billiards",
  "authors": [
    "Zainab Alsheekhhussain"
  ],
  "comment": "19",
  "journal": "Far East Journal of Dynamical Systems, 25 (2014), 123-147",
  "categories": [
    "math.DS"
  ],
  "abstract": "We investigate the rotation sets of open billiards in $\\mathbb{R}^N$ for the natural observable related to a starting point of a given billiard trajectory. We prove that the general rotation set is convex and the set of all convex combinations of rotation vectors of periodic trajectory $P_\\phi$ is dense in it. We provide a constructive proof which illustrates that the set $P_\\phi$ is dense in the pointwise rotation set, and the closure of the pointwise rotation set is convex. We also consider a class of billiards consisting of three obstacles and construct a sequence in the symbol space such that its rotation vector is not defined.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-29T01:35:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "open billiards",
      "pointwise rotation set",
      "rotation vector",
      "general rotation set",
      "symbol space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150507902A"
    }
  }
}