{
  "id": "1602.01938",
  "version": "v1",
  "published": "2016-02-05T07:34:38.000Z",
  "updated": "2016-02-05T07:34:38.000Z",
  "title": "On the measure-theoretic entropy and topological pressure of free semigroup actions",
  "authors": [
    "Xiaogang Lin",
    "Dongkui Ma",
    "Yupan Wang"
  ],
  "comment": "28 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we introduce the notions of topological pressure and measure-theoretic entropy for a free semigroup action. Suppose that a free semigroup acts on a compact metric space by continuous self-maps. To this action, we assign a skew-product transformation whose fiber topological pressure is taken to be the topological pressure of the initial action. Some properties of these two notions are given. Then we give two main results. One is the relationship between the topological pressure of the skew-product transformation and the topological pressure of the free semigroup action, the other is the partial variational principle about the topological pressure. Then we apply it to study the measure-theoretic entropy and the topological entropy of finite affine transformations on a metrizable group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-05T07:34:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "topological pressure",
      "free semigroup action",
      "measure-theoretic entropy",
      "skew-product transformation",
      "free semigroup acts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}