{
  "id": "2304.08148",
  "version": "v1",
  "published": "2023-04-17T10:57:34.000Z",
  "updated": "2023-04-17T10:57:34.000Z",
  "title": "Pentagram in the trajectory of bar billiards around a triangle",
  "authors": [
    "Takeo Noda",
    "Shin-ichi Yasutomi"
  ],
  "comment": "32 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider a bar billiards problem for a triangle in the unit circle. For the point on the unit circle, we construct a line from it in a counterclockwise direction tangent to the triangle, and examine a map corresponding to the point of intersection with the circle. We provide sufficient conditions for the rotation number $\\rho$ of this map to be $\\frac{2}{5}$, as well as necessary conditions for $\\rho=\\frac{2}{5}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-17T10:57:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37E10",
      "37E45",
      "51M09"
    ],
    "keywords": [
      "unit circle",
      "trajectory",
      "bar billiards problem",
      "necessary conditions",
      "sufficient conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}