{
  "id": "math/0507213",
  "version": "v1",
  "published": "2005-07-11T09:39:43.000Z",
  "updated": "2005-07-11T09:39:43.000Z",
  "title": "Contour integrals as $Ad$-invariant functions on the fundamental group",
  "authors": [
    "Marcin Bobienski"
  ],
  "comment": "13 pages",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "We introduce a general approach to contour integrals. It covers usual Abelian integrals, the higher order Melnikov integrals and the generalized Abelian integrals. We prove that the generating function always satisfies a linear differential equation of finite order. We also present a relationship between the generalized Abelian integral and certain representation of the fundamental group of complex curve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-07-11T09:39:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34C07",
      "34C08"
    ],
    "keywords": [
      "fundamental group",
      "contour integrals",
      "invariant functions",
      "generalized abelian integral",
      "covers usual abelian integrals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......7213B"
    }
  }
}