{
  "id": "2002.00853",
  "version": "v1",
  "published": "2020-02-03T15:59:56.000Z",
  "updated": "2020-02-03T15:59:56.000Z",
  "title": "The radial Julia set of $\\exp(z)-2$ is zero-dimensional",
  "authors": [
    "David S. Lipham"
  ],
  "comment": "4 pages",
  "categories": [
    "math.DS",
    "math.GN"
  ],
  "abstract": "Let $a\\in (-\\infty,-1)$, let $f_a$ be the complex exponential mapping $z\\mapsto e^z+a$, and let $J(f_a)$ denote the Julia set of $f_a$. We show the radial Julia set $\\{z\\in J(f_a):f_a^n(z)\\not\\to\\infty\\}$ has topological dimension zero. This improves a 2018 result by Vasiliki Evdoridou and Lasse Rempe-Gillen. We put $a=-2$ to see that for Fatou's function $f(z)=z+1+e^{-z}$, the entire non-escaping set $\\{z\\in \\mathbb C:f^n(z)\\not\\to\\infty\\}$ is zero-dimensional.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-03T15:59:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "30D05",
      "54F45"
    ],
    "keywords": [
      "radial julia set",
      "zero-dimensional",
      "topological dimension zero",
      "entire non-escaping set",
      "vasiliki evdoridou"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}