{
  "id": "1806.09306",
  "version": "v1",
  "published": "2018-06-25T07:23:08.000Z",
  "updated": "2018-06-25T07:23:08.000Z",
  "title": "Uniform positive recursion frequency of any minimal dynamical system on a compact space",
  "authors": [
    "Xiongping Dai"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Using Gottschalk's notion\\,---\\,weakly locally almost periodic point, we show in this paper that if $f\\colon X\\rightarrow X$ is a minimal continuous transformation of a compact Hausdorff space $X$ to itself, then for all entourage $\\varepsilon$ of $X$, \\begin{equation*} \\inf_{x\\in X}\\left\\{\\liminf_{N-M\\to\\infty}\\frac{1}{N-M}\\sum_{n=M}^{N-1}1_{\\varepsilon[x]}(f^nx)\\right\\}>0. \\end{equation*} An analogous assertion also holds for each minimal $C^0$-semiflow $\\pi\\colon \\mathbb{R}_+\\times X\\rightarrow X$ and for any minimal transformation group with discrete amenable phase group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-25T07:23:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "20M20"
    ],
    "keywords": [
      "uniform positive recursion frequency",
      "minimal dynamical system",
      "compact space",
      "discrete amenable phase group",
      "compact hausdorff space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}