{
  "id": "0910.1888",
  "version": "v1",
  "published": "2009-10-10T02:09:20.000Z",
  "updated": "2009-10-10T02:09:20.000Z",
  "title": "Ducks on the torus: existence and uniqueness",
  "authors": [
    "Ilya Schurov"
  ],
  "comment": "To appear in Journal of Dynamical and Control Systems, presumably Vol. 16 (2010), No. 2; The final publication is available at www.springerlink.com",
  "journal": "Journal of Dynamical and Control Systems, Vol. 16, Number 2, April 2010, 267-300",
  "doi": "10.1007/s10883-010-9093-9",
  "categories": [
    "math.DS",
    "math.CA"
  ],
  "abstract": "We show that there exist generic slow-fast systems with only one (time-scaling) parameter on the two-torus, which have canard cycles for arbitrary small values of this parameter. This is in drastic contrast with the planar case, where canards usually occur in two-parametric families. Here we treat systems with a convex slow curve. In this case there is a set of parameter values accumulating to zero for which the system has exactly one attracting and one repelling canard cycle. The basin of the attracting cycle is almost the whole torus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-10T02:09:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "70K70",
      "37G15"
    ],
    "keywords": [
      "uniqueness",
      "generic slow-fast systems",
      "arbitrary small values",
      "convex slow curve",
      "canards usually occur"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.1888S"
    }
  }
}