{
  "id": "1605.08903",
  "version": "v1",
  "published": "2016-05-28T15:36:11.000Z",
  "updated": "2016-05-28T15:36:11.000Z",
  "title": "On the Dynamics of Rational Maps with Two Free Critical Points",
  "authors": [
    "HyeGyong Jang",
    "Norbert Steinmetz"
  ],
  "comment": "12 pages, 4 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper we discuss the dynamical structure of the rational family $(f_t)$ given by $$f_t(z)=tz^{m}\\Big(\\frac{1-z}{1+z}\\Big)^{n}\\quad(m\\ge 2,~t\\ne 0).$$ Each map $f_t$ has two super-attracting immediate basins and two free critical points. We prove that for $0<|t|\\le 1$ and $|t|\\ge 1$, either of these basins is completely invariant and at least one of the free critical points is inactive. Based on this separation we draw a detailed picture the structure of the dynamical and the parameter plane.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-28T15:36:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "37F15",
      "37F45"
    ],
    "keywords": [
      "free critical points",
      "rational maps",
      "super-attracting immediate basins",
      "parameter plane",
      "dynamical structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}