{
  "id": "2201.01268",
  "version": "v2",
  "published": "2022-01-04T18:04:53.000Z",
  "updated": "2023-09-20T09:08:05.000Z",
  "title": "Geometrical representation of subshifts for primitive substitutions",
  "authors": [
    "Paul Mercat"
  ],
  "comment": "31 pages, 5 figures, preprint",
  "categories": [
    "math.DS"
  ],
  "abstract": "For any primitive substitution whose Perron eigenvalue is Pisot unit, we construct a domain exchange measurably conjugated to the subshift. And we give a condition for the subshift to be a finite extension of a torus translation. For the particular case of weakly irreducible Pisot substitution, we show that the subshift is either a finite extension of a torus translation, either a power of the subshift is weakly mixing. And we provide an algorithm to compute eigenvalues of the subshift associated to any primitive pseudo-unimodular substitution.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-09-20T09:08:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10",
      "37A05"
    ],
    "keywords": [
      "primitive substitution",
      "geometrical representation",
      "torus translation",
      "finite extension",
      "pisot unit"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}