{
  "id": "2205.11904",
  "version": "v1",
  "published": "2022-05-24T08:54:40.000Z",
  "updated": "2022-05-24T08:54:40.000Z",
  "title": "Some notes on variational principle for metric mean dimension",
  "authors": [
    "Rui Yang",
    "Ercai Chen",
    "Xiaoyao Zhou"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2203.12251",
  "categories": [
    "math.DS"
  ],
  "abstract": "Firstly, we answer the problem 1 asked by Gutman and $\\rm \\acute{\\ S}$piewak in \\cite{gs20}, then we establish a double variational principle for mean dimension in terms of R$\\bar{e}$nyi information dimension and show the order of $\\sup$ and $\\limsup$ (or $\\liminf$) of the variational principle for the metric mean dimension in terms of R$\\bar{e}$nyi information dimension obtained by Gutman and $\\rm \\acute{\\ S}$piewak can be changed under the marker property. Finally, we attempt to introduce the notion of maximal metric mean dimension measure, which is an analogue of the concept called classical maximal entropy measure related to the topological entropy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-24T08:54:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "variational principle",
      "nyi information dimension",
      "maximal metric mean dimension measure",
      "classical maximal entropy measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}