{
  "id": "2210.05256",
  "version": "v1",
  "published": "2022-10-11T08:36:13.000Z",
  "updated": "2022-10-11T08:36:13.000Z",
  "title": "Parametric linearization of skew products",
  "authors": [
    "Pierre Berger",
    "Bernhard Reinke"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We establish a linearization criterion for skew products of contractions in any dimension. We prove their smooth or holomorphic parameter dependence. In the smooth setting, we use the language of tame Fr\\'echet spaces. We apply our result to the linearization of totally projectively expanding Cantor sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-11T08:36:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "skew products",
      "parametric linearization",
      "holomorphic parameter dependence",
      "tame frechet spaces",
      "linearization criterion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}