{
  "id": "1607.04086",
  "version": "v1",
  "published": "2016-07-14T11:08:06.000Z",
  "updated": "2016-07-14T11:08:06.000Z",
  "title": "Averaging theory at any order for computing limit cycles of discontinuous piecewise differential systems with many zones",
  "authors": [
    "Jaume Llibre",
    "Douglas D. Novaes",
    "Camila A. B. Rodrigues"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "This work is devoted to study the existence of periodic solutions for a family of discontinuous differential systems $Z(x,y;\\epsilon)$ with many zones. We show that for $\\epsilon$ sufficiently small the averaged functions at any order control the existence of crossing limit cycles for systems in this family. We also provide some examples dealing with nonlinear centers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-14T11:08:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34C29",
      "34C25",
      "37G15",
      "34C07"
    ],
    "keywords": [
      "discontinuous piecewise differential systems",
      "computing limit cycles",
      "averaging theory",
      "nonlinear centers",
      "crossing limit cycles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}