{
  "id": "0903.4523",
  "version": "v1",
  "published": "2009-03-26T07:22:34.000Z",
  "updated": "2009-03-26T07:22:34.000Z",
  "title": "Oscillations near separatrix for perturbed Duffing equation",
  "authors": [
    "O. M. Kiselev"
  ],
  "comment": "17 pages, 4 figures",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP"
  ],
  "abstract": "A periodic perturbation generates a complicated dynamics close to separatrices and saddle points. We construct an asymptotic solution which is close to the separatrix for the unperturbed Duffing's oscillator over a long time. This solution is defined by a separatrix map. This map is obtained for any order of the perturbation parameter. Properties of this map show an instability of a motion for the perturbed system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-26T07:22:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "perturbed duffing equation",
      "oscillations",
      "periodic perturbation generates",
      "complicated dynamics close",
      "saddle points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.4523K"
    }
  }
}