{
  "id": "1002.4169",
  "version": "v2",
  "published": "2010-02-22T19:13:17.000Z",
  "updated": "2010-05-17T21:58:36.000Z",
  "title": "Canard Cycles and Poincaré Index of Non-Smooth Vector Fields on the Plane",
  "authors": [
    "Claudio Buzzi",
    "Tiago de Carvalho",
    "Paulo Ricardo da Silva"
  ],
  "comment": "20 pages, 25 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "This paper is concerned with closed orbits of non-smooth vector fields on the plane. For a subclass of non-smooth vector fields we provide necessary and sufficient conditions for the existence of canard kind solutions. By means of a regularization we prove that the canard cycles are singular orbits of singular perturbation problems which are limit periodic sets of a sequence of limit cycles. Moreover, we generalize the Poincar\\'e Index for non-smooth vector fields.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-05-17T21:58:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34C20",
      "34C26",
      "34D15",
      "34H05"
    ],
    "keywords": [
      "non-smooth vector fields",
      "canard cycles",
      "limit periodic sets",
      "singular perturbation problems",
      "canard kind solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.4169B"
    }
  }
}