{
  "id": "1603.07520",
  "version": "v1",
  "published": "2016-03-24T10:47:16.000Z",
  "updated": "2016-03-24T10:47:16.000Z",
  "title": "Cubic Perturbations of Symmetric elliptic Hamiltonians of degree four in a Complex domain",
  "authors": [
    "Bassem Ben Hamed",
    "Ameni Gargouri",
    "Lubomir Gavrilov"
  ],
  "comment": "17 pages, 5 figures in Bull. Sci. math. 2016. arXiv admin note: substantial text overlap with arXiv:1401.5419",
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider arbitrary one-parameter cubic deformations of the Duffing oscillator $x\"=x-x^3$. In the case when the first Melnikov function $M_1$ vanishes, but $M_2\\neq 0$ we compute the general form of $M_2$ and study its zeros in a suitable complex domain.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-24T10:47:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34C07",
      "37G15"
    ],
    "keywords": [
      "symmetric elliptic hamiltonians",
      "cubic perturbations",
      "arbitrary one-parameter cubic deformations",
      "first melnikov function",
      "suitable complex domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}