{
  "id": "2305.07925",
  "version": "v1",
  "published": "2023-05-13T14:36:37.000Z",
  "updated": "2023-05-13T14:36:37.000Z",
  "title": "Symmetric cubic polynomials",
  "authors": [
    "A. Blokh",
    "L. Oversteegen",
    "N. Selinger",
    "V. Timorin",
    "S. Vejandla"
  ],
  "comment": "34 pages, 3 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We describe a model $\\mathcal{M}_3^{comb}$ for the boundary of the connectedness locus $\\mathcal{M}^{sy}_3$ of the parameter space of cubic symmetric polynomials $p_c(z)=z^3-3c^2z$. We show that there exists a monotone continuous function $\\pi:\\partial \\mathcal{M}_c^{sy}\\to \\mathcal{M}_3^{comb}$ which is a homeomorphism if $\\mathcal{M}^{sy}_3$ is locally connected.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-13T14:36:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F20",
      "37F10"
    ],
    "keywords": [
      "symmetric cubic polynomials",
      "cubic symmetric polynomials",
      "connectedness locus",
      "parameter space",
      "monotone continuous function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}