{
  "id": "2304.07914",
  "version": "v1",
  "published": "2023-04-16T23:14:15.000Z",
  "updated": "2023-04-16T23:14:15.000Z",
  "title": "Reading multiplicity in unfoldings from epsilon-neighborhoods of orbits",
  "authors": [
    "Renato Huzak",
    "Pavao Mardešić",
    "Maja Resman",
    "Vesna Županović"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We consider generic 1-parameter unfoldings of parabolic vector fields. It is known that the box dimension of orbits of their time-one maps is discontinuous at the bifurcation value. Here, we expand asymptotically the Lebesgue measure of the epsilon-neighborhoods of orbits of the time-one maps in a Chebyshev scale, uniformly with respect to the bifurcation parameter. We use the so-called Ecalle-Roussarie-type compensators. We read from the expansion the number of hyperbolic points born in the unfolding of the parabolic point (i.e. the codimension of the bifurcation).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-16T23:14:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37G10",
      "34C23",
      "28A80",
      "37C45",
      "37M20"
    ],
    "keywords": [
      "reading multiplicity",
      "epsilon-neighborhoods",
      "time-one maps",
      "parabolic vector fields",
      "hyperbolic points born"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}