{
  "id": "2009.14511",
  "version": "v1",
  "published": "2020-09-30T08:57:03.000Z",
  "updated": "2020-09-30T08:57:03.000Z",
  "title": "Parameter spaces of locally constant cocycles",
  "authors": [
    "Argyrios Christodoulou"
  ],
  "comment": "21 pages, 10 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "This article concerns the locus of all locally constant $\\mathrm{SL}(2,\\mathbb{R})$-valued cocycles that are uniformly hyperbolic, called the hyperbolic locus. Using the theory of semigroups of M\\\"obius transformations we introduce a new locus in $\\mathrm{SL}(2,\\mathbb{R})^N$ which allows us to study the complement of the hyperbolic locus. Our results answer a question of Avila, Bochi and Yoccoz, and Jacques and Short, while motivating a new line of investigation on the subject.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-30T08:57:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D20",
      "30F45"
    ],
    "keywords": [
      "locally constant cocycles",
      "parameter spaces",
      "hyperbolic locus",
      "article concerns",
      "results answer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}