{
  "id": "1510.00853",
  "version": "v1",
  "published": "2015-10-03T18:03:42.000Z",
  "updated": "2015-10-03T18:03:42.000Z",
  "title": "Limit cycles for a class of $\\mathbb{Z}_{2n}-$equivariant systems without infinite equilibria",
  "authors": [
    "Isabel S. Labouriau",
    "Adrian C. Murza"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We analyze the dynamics of a class of $\\mathbb{Z}_{2n}$-equivariant differential equations on the plane, depending on 4 real parameters. This study is the generalisation to $\\mathbb{Z}_{2n}$ of previous works with $\\mathbb{Z}_4$ and $\\mathbb{Z}_6$ symmetry. We reduce the problem of finding limit cycles to an Abel equation, and provide criteria for proving in some cases uniqueness and hyperbolicity of the limit cycle that surrounds either 1, $2n+1$ or $4n+1$ equilibria, the origin being always one of these points.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-03T18:03:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34C07"
    ],
    "keywords": [
      "equivariant systems",
      "infinite equilibria",
      "equivariant differential equations",
      "abel equation",
      "cases uniqueness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}