{
  "id": "1809.06767",
  "version": "v1",
  "published": "2018-09-18T14:26:08.000Z",
  "updated": "2018-09-18T14:26:08.000Z",
  "title": "On Fatou and Julia sets of foliations",
  "authors": [
    "Taro Asuke"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "The Fatou-Julia decomposition is significant in the study of iterations of holomorphic mappings. Such a decomposition can be also considered for foliations in a unified manner. Although the decomposition will be fundamental in the study, it is not easy to decide the decomposition. In this article, we give a sufficient condition for open sets to be contained in Fatou sets. We also discuss relations between Fatou--Julia decompositions and minimal sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-18T14:26:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F75",
      "57R30",
      "32S65"
    ],
    "keywords": [
      "julia sets",
      "foliations",
      "fatou-julia decomposition",
      "fatou sets",
      "open sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}