{
  "id": "2103.09994",
  "version": "v1",
  "published": "2021-03-18T03:00:59.000Z",
  "updated": "2021-03-18T03:00:59.000Z",
  "title": "A Tits alternative for rational functions",
  "authors": [
    "Jason P. Bell",
    "Keping Huang",
    "Wayne Peng",
    "Thomas J. Tucker"
  ],
  "comment": "16 pages",
  "categories": [
    "math.NT",
    "math.AG",
    "math.GR"
  ],
  "abstract": "We prove an analog of the Tits alternative for rational functions. In particular, we show that if $S$ is a finitely generated semigroup of rational functions over the complex numbers, then either $S$ has polynomially bounded growth or $S$ contains a nonabelian free semigroup. We also show that if f and g are polarizable maps over any field that do not have the same set of preperiodic points, then the semigroup generated by f and g contains a nonabelian free semigroup.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-18T03:00:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20M05",
      "14H37",
      "20D15"
    ],
    "keywords": [
      "rational functions",
      "tits alternative",
      "nonabelian free semigroup",
      "complex numbers",
      "preperiodic points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}