{
  "id": "0907.2876",
  "version": "v3",
  "published": "2009-07-16T16:01:10.000Z",
  "updated": "2010-12-14T15:01:33.000Z",
  "title": "Bratteli-Vershik representations of some one-sided substitution subshifts",
  "authors": [
    "Reem Yassawi"
  ],
  "comment": "18 pages, 1 figure",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study one-sided substitution subshifts, and how they can be represented using Bratteli-Vershik systems. In particular we focus on minimal recognizable substitutions such that the generated one-sided substitution subshift contains only one non-shift-invertible element (a branch point), and we call these substitutions quasi-invertible. We give an algorithm to check whether a substitution is quasi-invertible, and show that any substitution with a rational Perron value is orbit equivalent to a quasi-invertible substitution. If the quasi-invertible substitution is left proper, then its subshift is equal to a substitution subshift where the original branch point is the new substitution fixed point. We use these results to prove that any reasonable quasi-invertible substitution subshift has a Bratteli-Vershik representation. We also give an example of a pair of substitutions whose 2-sided subshifts are topologically conjugate, while their 1-sided subshifts are not.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-12-14T15:01:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10"
    ],
    "keywords": [
      "bratteli-vershik representation",
      "quasi-invertible substitution",
      "generated one-sided substitution subshift contains",
      "original branch point",
      "study one-sided substitution subshifts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.2876Y"
    }
  }
}