{
  "id": "1309.5346",
  "version": "v4",
  "published": "2013-09-20T19:03:33.000Z",
  "updated": "2014-10-29T14:31:52.000Z",
  "title": "Limit cycles for a class of quintic $\\mathbb{Z}_6-$equivariant systems without infinite critical points",
  "authors": [
    "Maria Jesus Álvarez",
    "Isabel Salgado Labouriau",
    "Adrian Calin Murza"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We analyze the dynamics of a 4-parameter family of planar ordinary differential equations, given by a polynomial of degree 5 that is equivariant under a symmetry of order 6. We obtain the number of limit cycles as a function of the parameters, and provide criteria for proving in some cases uniqueness and hyperbolicity of the limit cycle surrounding either 1, 7 or 13 critical points, the origin being always one of these points. The method used is the reduction of the problem to an Abel equation.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-04-07T19:25:34.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2014-10-29T14:31:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34C07",
      "34C14",
      "34C23",
      "37C27"
    ],
    "keywords": [
      "limit cycle",
      "infinite critical points",
      "equivariant systems",
      "planar ordinary differential equations",
      "abel equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.5346A"
    }
  }
}