{
  "id": "1607.01271",
  "version": "v1",
  "published": "2016-07-05T14:37:12.000Z",
  "updated": "2016-07-05T14:37:12.000Z",
  "title": "Lyapunov exponents and related concepts for entire functions",
  "authors": [
    "Walter Bergweiler",
    "Xiao Yao",
    "Jianhua Zheng"
  ],
  "comment": "20 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $f$ be an entire function and denote by $f^\\#$ be the spherical derivative of $f$ and by $f^n$ the $n$-th iterate of $f$. For an open set $U$ intersecting the Julia set $J(f)$, we consider how fast $\\sup_{z\\in U} (f^n)^\\#(z)$ and $\\int_U (f^n)^\\#(z)^2 dx\\:dy$ tend to $\\infty$. We also study the growth rate of the sequence $(f^n)^\\#(z)$ for $z\\in J(f)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-05T14:37:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "entire function",
      "lyapunov exponents",
      "related concepts",
      "th iterate",
      "open set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}