{
  "id": "math/0305264",
  "version": "v1",
  "published": "2003-05-19T07:14:59.000Z",
  "updated": "2003-05-19T07:14:59.000Z",
  "title": "KAM Theorem for Gevrey Hamiltonians",
  "authors": [
    "Georgi Popov"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider Gevrey perturbations $H$ of a completely integrable Gevrey Hamiltonian $H_0$. Given a Cantor set $\\Omega_\\kappa$ defined by a Diophantine condition, we find a family of KAM invariant tori of $H$ with frequencies $\\omega\\in \\Omega_\\kappa$ which is Gevrey smooth in a Whitney sense. Moreover, we obtain a symplectic Gevrey normal form of the Hamiltonian in a neighborhood of the union $\\Lambda$ of the invariant tori. This leads to effective stability of the quasiperiodic motion near $\\Lambda$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-05-19T07:14:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kam theorem",
      "symplectic gevrey normal form",
      "kam invariant tori",
      "whitney sense",
      "cantor set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......5264P"
    }
  }
}