{
  "id": "1401.3932",
  "version": "v2",
  "published": "2014-01-16T08:43:13.000Z",
  "updated": "2014-04-24T20:43:59.000Z",
  "title": "Polynomial normal forms of Constrained Differential Equations with three parameters",
  "authors": [
    "H. Jardón-Kojakhmetov",
    "Henk Broer"
  ],
  "comment": "This is an updated and revised version. Minor modifications made",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study generic constrained differential equations (CDEs) with three parameters, thereby extending Takens's classification of singularities of such equations. In this approach, the singularities analyzed are the Swallowtail, the Hyperbolic, and the Elliptic Umbilics. We provide polynomial local normal forms of CDEs under topological equivalence. Generic CDEs are important in the study of slow-fast (SF) systems. Many properties and the characteristic behavior of the solutions of SF systems can be inferred from the corresponding CDE. Therefore, the results of this paper show a first approximation of the flow of generic SF systems with three slow variables.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-04-24T20:43:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "polynomial normal forms",
      "parameters",
      "study generic constrained differential equations",
      "sf systems",
      "polynomial local normal forms"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.jde.2014.04.022",
      "journal": "Journal of Differential Equations",
      "year": 2014,
      "month": "Aug",
      "volume": 257,
      "number": 4,
      "pages": 1012
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014JDE...257.1012J"
    }
  }
}