{
  "id": "1404.2630",
  "version": "v1",
  "published": "2014-04-09T21:19:18.000Z",
  "updated": "2014-04-09T21:19:18.000Z",
  "title": "Bifurcation of limit cycles from a non-smooth perturbation of a two-dimensional isochronous cylinder",
  "authors": [
    "Claudio A. Buzzi",
    "Rodrigo D. Euzebio",
    "Ana C. Mereu"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Detect the birth of limit cycles in non-smooth vector fields is a very important matter into the recent theory of dynamical systems and applied sciences. The goal of this paper is to study the bifurcation of limit cycles from a continuum of periodic orbits filling up a two-dimensional isochronous cylinder of a vector field in $\\mathbb{R}^{3}$. The approach involves the regularization process of non-smooth vector fields and a method based in the Malkin's bifurcation function for $C^{0}$ perturbations. The results provide sufficient conditions in order to obtain limit cycles emerging from the cylinder through smooth and non-smooth perturbations of it. To the best of our knowledge they also illustrate the implementation by the first time of a new method based in the Malkin's bifurcation function. In addition, some points concerning the number of limit cycles bifurcating from non-smooth perturbations compared with smooth ones are studied. In summary the results yield a better knowledge about limit cycles in non-smooth vector fields in $\\mathbb{R}^{3}$ and explicit a manner to obtain them by performing non-smooth perturbations in codimension one Euclidean manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-09T21:19:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "limit cycles",
      "two-dimensional isochronous cylinder",
      "non-smooth perturbation",
      "non-smooth vector fields",
      "malkins bifurcation function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.2630B"
    }
  }
}