{
  "id": "2107.07262",
  "version": "v1",
  "published": "2021-07-15T11:38:29.000Z",
  "updated": "2021-07-15T11:38:29.000Z",
  "title": "Quadratic rational maps with integer multipliers",
  "authors": [
    "Valentin Huguin"
  ],
  "comment": "17 pages, 4 figures, 6 tables",
  "categories": [
    "math.DS",
    "math.NT"
  ],
  "abstract": "In this article, we prove that every quadratic rational map whose multipliers all lie in the ring of integers of a given imaginary quadratic field is a power map, a Chebyshev map or a Latt\\`{e}s map. In particular, this provides some evidence in support of a conjecture by Milnor concerning rational maps whose multipliers are all integers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-15T11:38:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37P05",
      "37P35",
      "37F10",
      "37F44"
    ],
    "keywords": [
      "quadratic rational map",
      "integer multipliers",
      "imaginary quadratic field",
      "milnor concerning rational maps",
      "chebyshev map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}