{
  "id": "math/0109116",
  "version": "v2",
  "published": "2001-09-18T08:46:21.000Z",
  "updated": "2004-05-25T16:35:52.000Z",
  "title": "Closed characteristics on compact convex hypersurfaces in $\\R^{2n}$",
  "authors": [
    "Yiming Long",
    "Chaofeng Zhu"
  ],
  "comment": "52 pages, published version",
  "journal": "Ann. of Math. (2), Vol. 155 (2002), no. 2, 317--368",
  "categories": [
    "math.DS",
    "math.SG"
  ],
  "abstract": "For any given compact C^2 hypersurface \\Sigma in {\\bf R}^{2n} bounding a strictly convex set with nonempty interior, in this paper an invariant \\varrho_n(\\Sigma) is defined and satisfies \\varrho_n(\\Sigma)\\ge [n/2]+1, where [a] denotes the greatest integer which is not greater than a\\in {\\bf R}. The following results are proved in this paper. There always exist at least \\rho_n(\\Sigma) geometrically distinct closed characteristics on \\Sigma. If all the geometrically distinct closed characteristics on \\Sigma are nondegenerate, then \\varrho_n(\\Sigma)\\ge n. If the total number of geometrically distinct closed characteristics on \\Sigma is finite, there exists at least an elliptic one among them, and there exist at least \\varrho_n(\\Sigma)-1 of them possessing irrational mean indices. If this total number is at most 2\\varrho_n(\\Sigma) -2, there exist at least two elliptic ones among them.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-05-25T16:35:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58E05"
    ],
    "keywords": [
      "compact convex hypersurfaces",
      "geometrically distinct closed characteristics",
      "total number",
      "possessing irrational mean indices",
      "nonempty interior"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Princeton University and the Institute for Advanced Study",
      "journal": "Ann. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 52,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......9116L"
    }
  }
}