{
  "id": "1610.00317",
  "version": "v1",
  "published": "2016-10-02T17:26:38.000Z",
  "updated": "2016-10-02T17:26:38.000Z",
  "title": "Suspension of the Billiard maps in the Lazutkin's coordinate",
  "authors": [
    "Jianlu Zhang"
  ],
  "comment": "16 pages, 4 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper we proved that under the Lazutkin's coordinate, the billiard map can be interpolated by a time-1 flow of a Hamiltonian $H(x,p,t)$ which can be formally expressed by \\[ H(x,p,t)=p^{3/2}+p^{5/2}V(x,p^{1/2},t),\\quad(x,p,t)\\in\\T\\times[0,+\\infty)\\times\\T, \\] where $V(\\cdot,\\cdot,\\cdot)$ is $C^{r-5}$ smooth if the convex billiard boundary is $C^r$ smooth. Benefit from this suspension we can construct transitive trajectories between two adjacent caustics under a variational framework.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-02T17:26:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lazutkins coordinate",
      "billiard map",
      "suspension",
      "convex billiard boundary",
      "construct transitive trajectories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}