{
  "id": "1106.0857",
  "version": "v3",
  "published": "2011-06-04T20:45:40.000Z",
  "updated": "2012-12-12T15:07:42.000Z",
  "title": "On the number of limit cycles which appear by perturbation of two-saddle cycles of planar vector fields",
  "authors": [
    "Lubomir Gavrilov"
  ],
  "comment": "21 pages, 10 figures, a new section explaining the so called \"Petrov trick\" in the context of the paper is added. The paper will appear in \"Functional Analysis and Its Applications\" (2013)",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that every heteroclinic saddle loop (a two-saddle cycle) occurring in an analytic finite-parameter family of plane analytic vector fields, may generate no more than a finite number of limit cycles within the family.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2012-12-12T15:07:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34C07",
      "37G15",
      "70K05"
    ],
    "keywords": [
      "planar vector fields",
      "two-saddle cycle",
      "limit cycles",
      "plane analytic vector fields",
      "perturbation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.0857G"
    }
  }
}