{
  "id": "2109.11601",
  "version": "v3",
  "published": "2021-09-23T19:10:58.000Z",
  "updated": "2022-06-02T17:36:45.000Z",
  "title": "On amenability and measure of maximal entropy for semigroups of rational maps: II",
  "authors": [
    "Peter Makienko",
    "Carlos Cabrera"
  ],
  "comment": "25 pages",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "We compare dynamical and algebraic properties of semigroups of rational maps. In particular, we show a version of the Day-von Neumann's conjecture and give a partial positive answer to ``Sushkievich's problem'' for semigroups of rational maps. We also show the relation of these conjectures with Furstenberg's $\\times 2 \\times 3$ problem and prove a coarse version of Furstenberg's problem for semigroups of non-exceptional polynomials.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2022-06-02T17:36:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "30D05",
      "43A07"
    ],
    "keywords": [
      "rational maps",
      "maximal entropy",
      "semigroups",
      "amenability",
      "day-von neumanns conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}