{
  "id": "0806.2713",
  "version": "v2",
  "published": "2008-06-17T07:09:07.000Z",
  "updated": "2010-05-10T11:19:48.000Z",
  "title": "Generic hyperbolicity of equilibria and periodic orbits of the parabolic equation on the circle",
  "authors": [
    "Romain Joly",
    "Geneviève Raugel"
  ],
  "categories": [
    "math.AP",
    "math.DS"
  ],
  "abstract": "In this paper, we show that, for scalar reaction-diffusion equations on the circle S1, the property of hyperbolicity of all equilibria and periodic orbits is generic with respect to the non-linearity . In other words, we prove that in an appropriate functional space of nonlinear terms in the equation, the set of functions, for which all equilibria and periodic orbits are hyperbolic, is a countable intersection of open dense sets. The main tools in the proof are the property of the lap number and the Sard-Smale theorem.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-05-10T11:19:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic orbits",
      "generic hyperbolicity",
      "parabolic equation",
      "equilibria",
      "scalar reaction-diffusion equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.2713J"
    }
  }
}