{
  "id": "math/9908122",
  "version": "v1",
  "published": "1999-08-23T17:04:10.000Z",
  "updated": "1999-08-23T17:04:10.000Z",
  "title": "Limit Cycles and the Distribution of Zeros of Families of Analytic Functions",
  "authors": [
    "Alexander Brudnyi"
  ],
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "We estimate the expected number of limit cycles situated in a neighbourhood of the origin of a planar polynomial vector field. Our main tool is a distributional inequality for the number of zeros of some families of univariate holomorphic functions depending analytically on a parameter. We obtain this inequality by methods of Pluripotential Theory. This inequality also implies versions of a strong law of large numbers and the central limit theorem for a probabilistic scheme associated with the distribution of zeros.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-08-23T17:04:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34C05",
      "31C10",
      "60F05"
    ],
    "keywords": [
      "limit cycles",
      "analytic functions",
      "distribution",
      "holomorphic functions depending",
      "planar polynomial vector field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......8122B"
    }
  }
}