{
  "id": "1907.06626",
  "version": "v1",
  "published": "2019-07-15T17:57:31.000Z",
  "updated": "2019-07-15T17:57:31.000Z",
  "title": "On the complexity function for sequences which are not uniformly recurrent",
  "authors": [
    "Nic Ormes",
    "Ronnie Pavlov"
  ],
  "comment": "12 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that every non-minimal transitive subshift $X$ satisfying a mild aperiodicity condition satisfies $\\limsup c_n(X) - 1.5n = \\infty$, and give a class of examples which shows that the threshold of $1.5n$ cannot be increased. As a corollary, we show that any transitive $X$ satisfying $\\limsup c_n(X) - n = \\infty$ and $\\limsup c_n(X) - 1.5n < \\infty$ must be minimal. We also prove some restrictions on the structure of transitive non-minimal $X$ satisfying $\\liminf c_n(X) - 2n = -\\infty$, which imply unique ergodicity (for a periodic measure) as a corollary, which extends a result of Boshernitzan from the minimal case to the more general transitive case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-15T17:57:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complexity function",
      "uniformly recurrent",
      "mild aperiodicity condition satisfies",
      "general transitive case",
      "non-minimal transitive subshift"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}