{
  "id": "1707.00288",
  "version": "v1",
  "published": "2017-07-02T13:40:17.000Z",
  "updated": "2017-07-02T13:40:17.000Z",
  "title": "Area of the Fatou sets of a family of entire functions",
  "authors": [
    "Song Zhang",
    "Fei Yang"
  ],
  "comment": "15 pages, 1 figure",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $f$ be an entire function with the form $f(z)=P(e^z)/e^z$, where $P$ is a polynomial with degree at least $2$ and $P(0)\\neq 0$. We prove that the area of the Fatou set of $f$ in a horizontal strip of width $2\\pi$ is finite. In particular, the corresponding result can be applied to the sine family $\\alpha\\sin(z+\\beta)$, where $\\alpha\\neq 0$ and $\\beta\\in\\mathbb{C}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-02T13:40:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fatou set",
      "entire function",
      "horizontal strip",
      "polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}