{
  "id": "2107.01968",
  "version": "v1",
  "published": "2021-07-05T12:17:16.000Z",
  "updated": "2021-07-05T12:17:16.000Z",
  "title": "Some variational principles for the metric mean dimension of a semigroup action",
  "authors": [
    "Thomas Jacobus",
    "Fagner B. Rodrigues",
    "Marcus V. Silva"
  ],
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this manuscript we show that the metric mean dimension of a free semigroup action satisfies three variational principles: (a) the first one is based on a definition of Shapira's entropy, introduced in \\cite{SH} for a singles dynamics and extended for a semigroup action in this note; (b) the second one treats about a definition of Katok's entropy for a free semigroup action introduced in \\cite{CRV-IV}; (c) lastly we consider the local entropy function for a free semigroup action and show that the metric mean dimension satisfies a variational principle in terms of such function. Our results are inspired in the ones obtained by \\cite{LT2019}, \\cite{VV}, \\cite{GS1} and \\cite{RX}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-05T12:17:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A05",
      "37A35"
    ],
    "keywords": [
      "variational principle",
      "free semigroup action satisfies",
      "metric mean dimension satisfies",
      "local entropy function",
      "shapiras entropy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}