{
  "id": "1701.03276",
  "version": "v1",
  "published": "2017-01-12T09:34:44.000Z",
  "updated": "2017-01-12T09:34:44.000Z",
  "title": "Generic 1-parameter pertubations of a vector field with a singular point of codimension k",
  "authors": [
    "Arnaud Chéritat",
    "Chrisitane Rousseau"
  ],
  "comment": "47 pages, 23 figures",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "We describe the equivalence classes of germs of generic 1-parameter families of complex vector fields z dot = omega_epsilon(z) on C unfolding a singular point of multiplicity k+1: omega_0 = z^{k+1} + o(z^{k+1}). The equivalence is under conjugacy by holomorphic change of coordinate and parameter. We provide a description of the modulus space and (almost) unique normal forms. As a preparatory step, we present the complete bifurcation diagram of the family of vector fields z dot = z^{k+1} - epsilon, over CP1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-12T09:34:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "singular point",
      "codimension",
      "pertubations",
      "unique normal forms",
      "complex vector fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}