{
  "id": "2203.01122",
  "version": "v1",
  "published": "2022-03-02T14:20:06.000Z",
  "updated": "2022-03-02T14:20:06.000Z",
  "title": "Mean dimension of natural extension of algebraic systems",
  "authors": [
    "Bingbing Liang",
    "Ruxi Shi"
  ],
  "comment": "10pages. Comments welcome!",
  "categories": [
    "math.DS"
  ],
  "abstract": "Mean dimension may decrease after taking natural extension. In this paper we show that mean dimension stays the same after taking natural extension for an endomorphism on a compact metrizable abelian group. As an application, we obtain that the mean dimension of algebraic cellular automaton coincides with its natural extension, which strengthens a result of Burguet and Shi \\cite{BS21} with a different proof.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-02T14:20:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "natural extension",
      "algebraic systems",
      "algebraic cellular automaton coincides",
      "mean dimension stays",
      "compact metrizable abelian group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}