{
  "id": "1902.08130",
  "version": "v1",
  "published": "2019-02-21T16:37:27.000Z",
  "updated": "2019-02-21T16:37:27.000Z",
  "title": "Hyperbolicity of asymmetric lemon billiards",
  "authors": [
    "Xin Jin",
    "Pengfei Zhang"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Asymmetric lemon billiards was introduced in [CMZZ], where the billiard table $Q(r,b,R)$ is the intersection of two round disks with radii $r\\le R$, respectively, and $b$ measures the distance between the two centers. The boundary consists of two circular arcs $\\Gamma_r$ and $\\Gamma_R$. It is conjectured [BZZ] that the asymmetric lemon billiards is hyperbolic when the arc $\\Gamma_r$ is a major arc and $R$ is large. In this paper we prove this conjecture for sufficiently large $R$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-21T16:37:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymmetric lemon billiards",
      "hyperbolicity",
      "boundary consists",
      "circular arcs",
      "major arc"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}