{
  "id": "2212.03661",
  "version": "v1",
  "published": "2022-12-07T14:23:59.000Z",
  "updated": "2022-12-07T14:23:59.000Z",
  "title": "Rational maps with integer multipliers",
  "authors": [
    "Xavier Buff",
    "Thomas Gauthier",
    "Valentin Huguin",
    "Jasmin Raissy"
  ],
  "comment": "6 pages",
  "categories": [
    "math.DS",
    "math.CV"
  ],
  "abstract": "Let $O_K$ be the ring of integers of an imaginary quadratic field. Recently, Zhuchao Ji and Junyi Xie proved that rational maps whose multipliers at all periodic points belong to $O_K$ are power maps, Chebyshev maps or Latt\\`es maps. Their proof relies on a non-archimedean result by Benedetto, Ingram, Jones and Levy. In this note, we show that one may avoid using this non-archimedean result by considering a differential equation instead.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-07T14:23:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37P35",
      "37F10",
      "37P05"
    ],
    "keywords": [
      "rational maps",
      "integer multipliers",
      "non-archimedean result",
      "imaginary quadratic field",
      "periodic points belong"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}