{
  "id": "1802.04935",
  "version": "v1",
  "published": "2018-02-14T02:44:18.000Z",
  "updated": "2018-02-14T02:44:18.000Z",
  "title": "Multiplicity of closed characteristics on $P$-symmetric compact convex hypersurfaces in $\\mathbb{R}^{2n}$",
  "authors": [
    "Lei Liu",
    "Li Wu"
  ],
  "comment": "15 pages with 0 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we provide new index estimations and prove that for any $P$-symmetric compact convex hypersurface $\\Sigma$ in $\\mathbb{R}^{2n}$, i.e. $x\\in\\Sigma$ implies $Px\\in\\Sigma$ with a certain orthogonal symplectic matrix $P$, there are at least $[\\frac{3n}{4}]$ closed characteristics on $\\Sigma$. Provided there exist an integer $m>2$ such that $$P^m=I_{2n},$$ and there exist only one $\\theta\\in(0,\\pi]$ s.t. $e^{\\sqrt{-1}\\theta}\\in\\sigma(P)$ which satisfies $$S^+_P(e^{\\sqrt{-1}\\theta})=S^-_P(e^{\\sqrt{-1}\\theta}),$$ where $S^{\\pm}_P(\\omega)$ are the splitting numbers of $P$ at $\\omega\\in \\mathbf{U}:=\\{z\\in\\mathbb{C},|z|=1\\}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-14T02:44:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58E05",
      "37J45",
      "34C25",
      "37C75"
    ],
    "keywords": [
      "symmetric compact convex hypersurface",
      "closed characteristics",
      "multiplicity",
      "orthogonal symplectic matrix",
      "index estimations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}