{
  "id": "2008.13689",
  "version": "v1",
  "published": "2020-08-31T15:48:33.000Z",
  "updated": "2020-08-31T15:48:33.000Z",
  "title": "On symbolic factors of $\\cS$-adic subshifts of finite alphabet rank",
  "authors": [
    "Bastián Espinoza"
  ],
  "comment": "19 pages, 1 figure",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this article, we prove two results about minimal $\\cS$-adic subshifts with finite alphabet rank: 1. they have finite topological rank, and 2. symbolic factors between systems of this kind are always almost constant-to-1. Both results are consequence of some rigidity properties of the underlying combinatorics of words in this class of subshifts. As a corollary of the first result, we answer a question of Donoso, Durand, Maass and Petite.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-31T15:48:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10"
    ],
    "keywords": [
      "finite alphabet rank",
      "adic subshifts",
      "symbolic factors",
      "finite topological rank",
      "rigidity properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}