{
  "id": "2410.20998",
  "version": "v1",
  "published": "2024-10-28T13:21:57.000Z",
  "updated": "2024-10-28T13:21:57.000Z",
  "title": "Spiders' webs in the Eremenko-Lyubich class",
  "authors": [
    "Lasse Rempe"
  ],
  "comment": "8 pages",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "Consider the entire function $f(z)=\\cosh(z)$. We show that the escaping set of this function - that is, the set of points whose orbits tend to infinity under iteration - has a structure known as a \"spider's web\". This disproves a conjecture of Sixsmith from 2020. In fact, we show that the \"fast escaping set\", i.e. the set of points whose orbits tend to infinity at an iterated exponential rate, is a spider's web. This answers a question of Rippon and Stallard from 2012. We also discuss a wider class of functions to which our results apply, and state some open questions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-28T13:21:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "30D05"
    ],
    "keywords": [
      "eremenko-lyubich class",
      "orbits tend",
      "spiders web",
      "open questions",
      "wider class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}