{
  "id": "2009.13654",
  "version": "v1",
  "published": "2020-09-28T22:03:22.000Z",
  "updated": "2020-09-28T22:03:22.000Z",
  "title": "Strong Orbit Equivalence and Superlinear Complexity",
  "authors": [
    "Paulina Cecchi Bernales",
    "Sebastián Donoso"
  ],
  "comment": "18 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We show that within any strong orbit equivalent class, there exist minimal subshifts with arbitrarily low superlinear complexity. This is done by proving that for any simple dimension group with unit $(G,G^+,u)$ and any sequence of positive numbers $(p_n)_{n\\in\\mathbb{N}}$ such that $\\lim n/p_n=0$, there exist a minimal subshift whose dimension group is order isomorphic to $(G,G^+,u)$ and whose complexity function grows slower than $p_n$. As a consequence, we get that any Choquet simplex can be realized as the set of invariant measures of a minimal Toeplitz subshift whose complexity grows slower than $p_n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-28T22:03:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B10",
      "54H20"
    ],
    "keywords": [
      "strong orbit equivalence",
      "strong orbit equivalent class",
      "complexity function grows slower",
      "minimal subshift",
      "complexity grows slower"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}