{
  "id": "math/0207026",
  "version": "v1",
  "published": "2002-07-02T19:34:54.000Z",
  "updated": "2002-07-02T19:34:54.000Z",
  "title": "Integrability, hyperbolic flows and the Birkhoff normal form",
  "authors": [
    "M. Rouleux"
  ],
  "comment": "34 pages",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove that a Hamiltonian $p\\in C^\\infty(T^*{\\bf R}^n)$ is locally integrable near a non-degenerate critical point $\\rho_0$ of the energy, provided that the fundamental matrix at $\\rho_0$ has no purely imaginary eigenvalues. This is done by using Birkhoff normal forms, which turn out to be convergent in the $C^\\infty$ sense. We also give versions of the Lewis-Sternberg normal form near a hyperbolic fixed point of a canonical transformation. Then we investigate the almost holomorphic case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-07-02T19:34:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "birkhoff normal form",
      "hyperbolic flows",
      "integrability",
      "lewis-sternberg normal form",
      "fundamental matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......7026R"
    }
  }
}