{
  "id": "1508.05952",
  "version": "v1",
  "published": "2015-08-24T20:14:32.000Z",
  "updated": "2015-08-24T20:14:32.000Z",
  "title": "On the number of ergodic measures for minimal shifts with eventually constant complexity growth",
  "authors": [
    "Michael Damron",
    "Jon Fickenscher"
  ],
  "comment": "30 pages, 6 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "In 1985, Boshernitzan showed that a minimal (sub)shift satisfying a linear block growth condition must have a bounded number of ergodic probability measures. Recently, this bound was shown to be sharp through examples constructed by Cyr and Kra. In this paper, we show that under the stronger assumption of eventually constant growth, an improved bound exists. To this end, we introduce special Rauzy graphs. Variants of the well-known Rauzy graphs from symbolic dynamics, these graphs provide an explicit description of how a Rauzy graph for words of length n relates to the one for words of length n+1 for each n = 1,2,3...",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-24T20:14:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10",
      "37A25",
      "68R15"
    ],
    "keywords": [
      "eventually constant complexity growth",
      "minimal shifts",
      "ergodic measures",
      "linear block growth condition",
      "ergodic probability measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150805952D"
    }
  }
}