{
  "id": "2004.12976",
  "version": "v1",
  "published": "2020-04-27T17:42:27.000Z",
  "updated": "2020-04-27T17:42:27.000Z",
  "title": "Erdős space in Julia sets",
  "authors": [
    "David Sumner Lipham"
  ],
  "comment": "6 pages",
  "categories": [
    "math.DS",
    "math.GN"
  ],
  "abstract": "Let $\\dot E_{\\text{Im}}$ be set of endpoints of the Julia set of $\\exp(z)-1$ whose forward orbits escape to infinity in the imaginary direction. We prove $\\dot E_{\\text{Im}}$ is homeomorphic to Erd\\H{o}s space $\\mathfrak E:=\\{x\\in \\ell^2:x_n\\in \\mathbb Q\\text{ for all }n<\\omega\\}.$ This result extends to all complex exponential functions $\\exp(z)+a$ which have attracting or parabolic periodic orbits.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-27T17:42:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "30D05",
      "54F45"
    ],
    "keywords": [
      "julia set",
      "erdős space",
      "parabolic periodic orbits",
      "complex exponential functions",
      "forward orbits escape"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}