{
  "id": "2401.11309",
  "version": "v1",
  "published": "2024-01-20T19:43:12.000Z",
  "updated": "2024-01-20T19:43:12.000Z",
  "title": "Uniform boundedness on rational maps with automorphisms",
  "authors": [
    "Minsik Han"
  ],
  "comment": "13 pages",
  "categories": [
    "math.NT",
    "math.DS"
  ],
  "abstract": "In this paper, we study the dynamical uniform boundedness principle over a family of rational maps with certain nontrivial automorphisms. Specifically, we consider a family of rational maps of an arbitrary degree $d\\ge 2$ whose automorphism group contains the cyclic group of order $d$. We prove that a subfamily of this family satisfies the dynamical uniform boundedness principle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-20T19:43:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37P05"
    ],
    "keywords": [
      "rational maps",
      "dynamical uniform boundedness principle",
      "automorphism group contains",
      "arbitrary degree",
      "cyclic group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}