{
  "id": "1004.3410",
  "version": "v2",
  "published": "2010-04-20T11:16:01.000Z",
  "updated": "2010-09-07T10:26:42.000Z",
  "title": "Dynamics near manifolds of equilibria of codimension one and bifurcation without parameters",
  "authors": [
    "Stefan Liebscher"
  ],
  "comment": "corrected typos, minor clarifications in the formulation of the main theorem",
  "journal": "Electronic Journal of Differential Equations 2011(63):1-12 (2011)",
  "categories": [
    "math.DS"
  ],
  "abstract": "We investigate the breakdown of normal hyperbolicity of a manifold of equilibria of a flow. In contrast to classical bifurcation theory we assume the absence of any flow-invariant foliation at the singularity transverse to the manifold of equilibria. We call this setting bifurcation without parameters. In the present paper we provide a description of general systems with a manifold of equilibria of codimension one as a first step towards a classification of bifurcations without parameters. This is done by relating the problem to singularity theory of maps.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-09-07T10:26:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34C23",
      "34C20",
      "58K05"
    ],
    "keywords": [
      "equilibria",
      "parameters",
      "codimension",
      "classical bifurcation theory",
      "normal hyperbolicity"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.3410L"
    }
  }
}