{
  "id": "1911.09406",
  "version": "v1",
  "published": "2019-11-21T11:06:33.000Z",
  "updated": "2019-11-21T11:06:33.000Z",
  "title": "Perturbations of graphs for Newton maps",
  "authors": [
    "Yan Gao",
    "Hongming Nie"
  ],
  "comment": "23 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the convergence of graphs consisting of finitely many internal rays for degenerating Newton maps. We state a sufficient condition to guarantee the convergence. As an application, we investigate the boundedness of hyperbolic components in the moduli space of quartic Newton maps. We prove that such a hyperbolic component is bounded if and only if every element has degree $2$ on the immediate basin of each root.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-21T11:06:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperbolic component",
      "perturbations",
      "quartic newton maps",
      "degenerating newton maps",
      "sufficient condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}