{
  "id": "1202.3836",
  "version": "v3",
  "published": "2012-02-17T03:45:45.000Z",
  "updated": "2012-07-28T16:27:00.000Z",
  "title": "On curvature and hyperbolicity of monotone Hamiltonian systems",
  "authors": [
    "Paul W. Y. Lee"
  ],
  "comment": "34 pages, some typos are fixed in the new version",
  "categories": [
    "math.DS"
  ],
  "abstract": "Assume that a Hamiltonian system is monotone. In this paper, we give several characterizations on when such a system is Anosov. Assuming that a monotone Hamiltonian system has no conjugate point, we show that there are two distributions which are invariant under the Hamiltonian flow. We show that a monotone Hamiltonian flow without conjugate point is Anosov if and only if these distributions are transversal. We also show that if the reduced curvature of the Hamiltonian system is non-positive, then the flow is Anosov if and only if the reduced curvature is negative somewhere along each trajectory.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-07-28T16:27:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D20"
    ],
    "keywords": [
      "monotone hamiltonian system",
      "hyperbolicity",
      "conjugate point",
      "monotone hamiltonian flow",
      "reduced curvature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.3836L"
    }
  }
}