{
  "id": "1910.11694",
  "version": "v1",
  "published": "2019-10-24T01:01:12.000Z",
  "updated": "2019-10-24T01:01:12.000Z",
  "title": "Elliptic and non-hyperbolic closed characteristics on compact convex P-cyclic symmetric hypersurfaces in ${\\bf R}^{2n}$",
  "authors": [
    "Hui Liu",
    "Chongzhi Wang",
    "Duanzhi Zhang"
  ],
  "comment": "24 Pages. arXiv admin note: text overlap with arXiv:0812.0041 by other authors",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $\\Sigma$ be a compact convex hypersurface in ${\\bf R}^{2n}$ which is P-cyclic symmetric, i.e., $x\\in \\Sigma$ implies $Px\\in\\Sigma$ with P being a $2n\\times2n$ symplectic orthogonal matrix and $P^k=I_{2n}$, where $n, k\\geq2$, $ker(P-I_{2n})=0$. In this paper, we first generalize Ekeland index theory for periodic solutions of convex Hamiltonian system to a index theory with P boundary value condition and study its relationship with Maslov P-index theory, then we use index theory to prove the existence of elliptic and non-hyperbolic closed characteristics on compact convex P-cyclic symmetric hypersurfaces in ${\\bf R}^{2n}$ for a broad class of symplectic orthogonal matrix P.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-24T01:01:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58E05",
      "37J45",
      "34C25"
    ],
    "keywords": [
      "compact convex p-cyclic symmetric hypersurfaces",
      "non-hyperbolic closed characteristics",
      "generalize ekeland index theory",
      "symplectic orthogonal matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}