{
  "id": "2412.15281",
  "version": "v1",
  "published": "2024-12-18T09:53:20.000Z",
  "updated": "2024-12-18T09:53:20.000Z",
  "title": "Minimal subshifts of prescribed mean dimension over general alphabets",
  "authors": [
    "Xiangtong Wang",
    "Hang Zhao"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2101.01458 by other authors",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $G$ be a countable infinite amenable group, $K$ a finite-dimensional compact metrizable space, and $(K^G,\\sigma)$ the full $G$-shift on $K^G$. For any $r\\in [0,{\\rm mdim}(K^G,\\sigma))$, we construct a minimal subshift $(X,\\sigma)$ of $(K^G,\\sigma)$ with mdim$(X,\\sigma)=r$. Furthermore, we construct a subshift of $([0,1]^G,\\sigma)$ such that its mean dimension is $1$, and that the set of all attainable values of the mean dimension of its minimal subsystems is exactly the interval $[0,1)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-18T09:53:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "54F45"
    ],
    "keywords": [
      "prescribed mean dimension",
      "minimal subshift",
      "general alphabets",
      "finite-dimensional compact metrizable space",
      "minimal subsystems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}