{
  "id": "2103.13535",
  "version": "v1",
  "published": "2021-03-25T00:11:08.000Z",
  "updated": "2021-03-25T00:11:08.000Z",
  "title": "Convergence of the Birkhoff normal form sometimes implies convergence of a normalizing transformation",
  "authors": [
    "Rafael de la Llave",
    "Maria Saprykina"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Consider an analytic Hamiltonian system near its analytic invariant torus $\\mathcal T_0$ carrying zero frequency. We assume that the Birkhoff normal form of the Hamiltonian at $\\mathcal T_0$ is convergent and has a particular form: it is an analytic function of its non-degenerate quadratic part. We prove that in this case there is an analytic canonical transformation -- not just a formal power series -- bringing the Hamiltonian into its Birkhoff normal form.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-25T00:11:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "birkhoff normal form",
      "implies convergence",
      "normalizing transformation",
      "analytic hamiltonian system",
      "analytic invariant torus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}