{
  "id": "2211.11235",
  "version": "v1",
  "published": "2022-11-21T07:57:18.000Z",
  "updated": "2022-11-21T07:57:18.000Z",
  "title": "Measure transfer and $S$-adic developments for subshifts",
  "authors": [
    "Nicolas Bédaride",
    "Arnaud Hilion",
    "Martin Lustig"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Based on previous work of the authors, to any $S$-adic development of a subshift $X$ a \"directive sequence\" of commutative diagrams is associated, which consists at every level $n \\geq 0$ of the measure cone and the letter frequency cone of the level subshift $X_n$ associated canonically to the given $S$-adic development. The issuing rich picture enables one to deduce results about $X$ with unexpected directness. For instance, we exhibit a large class of minimal subshifts with entropy zero that all have infinitely many ergodic probability measures. As a side result we also exhibit, for any integer $d \\geq 2$, an $S$-adic development of a minimal, aperiodic, uniquely ergodic subshift $X$, where all level alphabets ${\\cal A}_n$ have cardinality $d\\,$, while none of the $d-2$ bottom level morphisms is recognizable in its level subshift $X_n \\subset {\\cal A}_n^\\mathbb Z$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-21T07:57:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10",
      "37A25",
      "37E25"
    ],
    "keywords": [
      "adic development",
      "measure transfer",
      "level subshift",
      "ergodic probability measures",
      "issuing rich picture enables"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}