{
  "id": "2206.10102",
  "version": "v1",
  "published": "2022-06-21T04:15:16.000Z",
  "updated": "2022-06-21T04:15:16.000Z",
  "title": "Existence of the Mandelbrot set in parameter planes for some generalized McMullen maps",
  "authors": [
    "Suzanne Boyd",
    "Alexander Mitchell"
  ],
  "comment": "34 pages, 22 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper we study rational functions of the form $ R_{n,a,c}(z) = z^n + \\dfrac{a}{z^n} + c, $ and hold either $a$ or $c$ fixed while the other varies. We show that for certain ranges of $a$, the $c$-parameter plane contains homeomorphic copies of the Mandelbrot set, as well as the $a$-plane for certain ranges of $c$. We use techniques first introduced by Douady and Hubbard, that were applied for the subfamily $R_{n,a,0}$ by Robert Devaney. These techniques involve polynomial-like maps of degree two.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-21T04:15:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "37F46"
    ],
    "keywords": [
      "generalized mcmullen maps",
      "mandelbrot set",
      "parameter plane contains homeomorphic copies",
      "study rational functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}