{
  "id": "1806.09132",
  "version": "v1",
  "published": "2018-06-24T11:42:37.000Z",
  "updated": "2018-06-24T11:42:37.000Z",
  "title": "Ergodic Properties of Tame Dynamical Systems",
  "authors": [
    "A. V. Romanov"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the problem on the weak-star decomposability of a topological $\\mathbb{N}_{0}$-dynamical system $(\\Omega,\\varphi)$, where $\\varphi$ is an endomorphism of a metric compact set $\\Omega$, into ergodic components in terms of the associated enveloping semigroups. In the tame case (where the Ellis semigroup $E(\\Omega,\\varphi)$ consists of $B_{1}$-transformations $\\Omega\\rightarrow \\Omega$), we show that (i) the desired decomposition exists for an appropriate choice of the generalized sequential averaging method; (ii) every sequence of weighted ergodic means for the shift operator $x\\rightarrow x\\circ\\varphi$, $x\\in C(\\Omega)$, contains a pointwise convergent subsequence. We also discuss the relationship between the statistical properties of $(\\Omega,\\varphi)$ and the mutual structure of minimal sets and ergodic measures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-24T11:42:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A30",
      "47A35",
      "20M20"
    ],
    "keywords": [
      "tame dynamical systems",
      "ergodic properties",
      "metric compact set",
      "ergodic measures",
      "ergodic components"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}