{
  "id": "0812.2226",
  "version": "v1",
  "published": "2008-12-11T19:23:30.000Z",
  "updated": "2008-12-11T19:23:30.000Z",
  "title": "Asymptotic expansion of planar canard solutions near a non-generic turning point",
  "authors": [
    "Thomas Forget"
  ],
  "categories": [
    "math.DS",
    "math.OC"
  ],
  "abstract": "This paper deals with the asymptotic study of the so-called canard solutions, which arise in the study of real singularly perturbed ODEs. Starting near an attracting branch of the \"slow curve\", those solutions are crossing a turning point before following for a while a repelling branch of the \"slow curve\". Assuming that the turning point is degenerate (or non-generic), we apply a correspondence presented in a recent paper. This application needs the definition of a family of functions $\\phi$ that is studied in a first part. Then, we use the correspondence is used to compute the asymptotic expansion in the powers of the small parameter for the canard solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-12-11T19:23:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "planar canard solutions",
      "non-generic turning point",
      "asymptotic expansion",
      "slow curve",
      "real singularly perturbed odes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.2226F"
    }
  }
}