{
  "id": "2210.10385",
  "version": "v1",
  "published": "2022-10-19T08:53:15.000Z",
  "updated": "2022-10-19T08:53:15.000Z",
  "title": "Iterated Monodromy Groups of Entire Maps and Dendroid Automata",
  "authors": [
    "Bernhard Reinke"
  ],
  "categories": [
    "math.DS",
    "math.GR"
  ],
  "abstract": "This paper discusses iterated monodromy groups for transcendental functions. We show that for every post-singularly finite entire transcendental function, the iterated monodromy action can be described by bounded activity automata of a special form, called \"dendroid automata\". In particular, we conclude that the iterated monodromy group of a post-singularly finite entire function is amenable if and only if the monodromy group is.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-19T08:53:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "37B10",
      "20E08"
    ],
    "keywords": [
      "dendroid automata",
      "entire maps",
      "post-singularly finite entire transcendental function",
      "paper discusses iterated monodromy groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}