{
  "id": "1912.12005",
  "version": "v1",
  "published": "2019-12-27T06:53:08.000Z",
  "updated": "2019-12-27T06:53:08.000Z",
  "title": "On the iterations and the argument distribution of meromorphic functions",
  "authors": [
    "Jianhua Zheng",
    "Jie Ding"
  ],
  "comment": "28 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "This paper consists of tow parts. One is to study the existence of a point $a$ in the intersection of Julia set and escaping set such that $\\arg z=\\theta$ is a singular direction if $\\theta$ is a limit point of $\\{\\arg f^n(a)\\}$ under some growth condition of a meromorphic function. The other is to study the connection between the Fatou set and singular direction. We prove that the absent of singular direction deduces the non-existence of annuli in the Fatou set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-27T06:53:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10"
    ],
    "keywords": [
      "meromorphic function",
      "argument distribution",
      "iterations",
      "fatou set",
      "singular direction deduces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}