{
  "id": "1601.00431",
  "version": "v1",
  "published": "2016-01-04T09:55:23.000Z",
  "updated": "2016-01-04T09:55:23.000Z",
  "title": "Integrability and strong normal forms for non-autonomous systems in a neighbourhood of an equilibrium",
  "authors": [
    "Alessandro Fortunati",
    "Stephen Wiggins"
  ],
  "comment": "10 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "The paper deals with the problem of existence of a convergent \"strong\" normal form in the neighbourhood of an equilibrium, for a finite dimensional system of differential equations with analytic and time-dependent non-linear term. The problem can be solved either under some non-resonance hypotheses on the spectrum of the linear part or if the non-linear term is assumed to be (slowly) decaying in time. This paper \"completes\" a pioneering work of Pustil'nikov in which, despite under weaker non-resonance hypotheses, the nonlinearity is required to be asymptotically autonomous. The result is obtained as a consequence of the existence of a strong normal form for a suitable class of real-analytic Hamiltonians with non-autonomous perturbations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-04T09:55:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37J40",
      "37B55",
      "37J25"
    ],
    "keywords": [
      "strong normal form",
      "non-autonomous systems",
      "neighbourhood",
      "equilibrium",
      "integrability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160100431F"
    }
  }
}