{
  "id": "1606.02581",
  "version": "v1",
  "published": "2016-06-08T14:38:05.000Z",
  "updated": "2016-06-08T14:38:05.000Z",
  "title": "Length of epsilon-neighborhoods of orbits of Dulac maps",
  "authors": [
    "P. Mardesic",
    "M. Resman",
    "J. -P. Rolin",
    "V. Zupanovic"
  ],
  "comment": "43 pages, 1 figure",
  "categories": [
    "math.DS"
  ],
  "abstract": "Dulac maps are first return maps of hyperbolic polycycles of analytic planar vector fields. We study the fractal properties of their orbits. For this purpose, we introduce a new notion, the \\emph{continuous time length of $\\varepsilon$-neighborhoods of the orbits}, and prove that this function of $\\varepsilon$ admits an asympotic expansion in terms of transseries. Given a parabolic Dulac germ, we prove that this expansion determines its class of formal conjugacy, and compute its Fatou coordinate.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-08T14:38:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34C20",
      "37C10",
      "39B12",
      "46A19",
      "28A75",
      "58K50",
      "26A12"
    ],
    "keywords": [
      "dulac maps",
      "epsilon-neighborhoods",
      "analytic planar vector fields",
      "parabolic dulac germ",
      "first return maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}