{
  "id": "0808.3028",
  "version": "v2",
  "published": "2008-08-22T03:39:21.000Z",
  "updated": "2012-02-27T23:13:31.000Z",
  "title": "Nonautonomous Hamiltonian Systems and Morales-Ramis Theory I. The Case $\\ddot{x}=f(x,t)$",
  "authors": [
    "Primitivo B. Acosta-Humanez"
  ],
  "comment": "15 pages without figures (19 pages and 6 figures in the published version)",
  "journal": "SIAM J. Appl. Dyn. Syst. 8, pp. 279-297, (2009)",
  "doi": "10.1137/080730329",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper we present an approach towards the comprehensive analysis of the non-integrability of differential equations in the form $\\ddot x=f(x,t)$ which is analogous to Hamiltonian systems with 1+1/2 degree of freedom. In particular, we analyze the non-integrability of some important families of differential equations such as Painlev\\'e II, Sitnikov and Hill-Schr\\\"odinger equation. We emphasize in Painlev\\'e II, showing its non-integrability through three different Hamiltonian systems, and also in Sitnikov in which two different version including numerical results are shown. The main tool to study the non-integrability of these kind of Hamiltonian systems is Morales-Ramis theory. This paper is a very slight improvement of the talk with the almost-same title delivered by the author in SIAM Conference on Applications of Dynamical Systems 2007.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-02-27T23:13:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37J30",
      "12H05",
      "70H07"
    ],
    "keywords": [
      "nonautonomous hamiltonian systems",
      "morales-ramis theory",
      "non-integrability",
      "differential equations",
      "slight improvement"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "SIAM Journal on Applied Dynamical Systems",
      "year": 2009,
      "month": "Jan",
      "volume": 8,
      "number": 1,
      "pages": 279
    },
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009SJADS...8..279A"
    }
  }
}