{
  "id": "1806.05811",
  "version": "v1",
  "published": "2018-06-15T05:43:02.000Z",
  "updated": "2018-06-15T05:43:02.000Z",
  "title": "Almost automorphy of invertible semiflows with compact Hausdorff phase spaces",
  "authors": [
    "Xiongping Dai"
  ],
  "comment": "26 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $T\\times X\\rightarrow X, (t,x)\\mapsto tx$ be a minimal semiflow on a compact Hausdorff space $X$ with phase semigroup $T$ such that each $t\\in T$ is an invertible map of $X$. An $x\\in X$ is called an \\textit{a.a. point} of $(T,X)$ if $(t_nx, t_n^{-1}y)\\to(y, x^\\prime)$ implies $x=x^\\prime$ for every net $\\{t_n\\}$ in $T$. In this paper, we study the a.a. dynamics of invertible semiflows; and moreover, we first present a complete proof of Veech's structure theorem of an a.a. flow.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-15T05:43:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "37B20",
      "20M20"
    ],
    "keywords": [
      "compact hausdorff phase spaces",
      "invertible semiflows",
      "automorphy",
      "compact hausdorff space",
      "veechs structure theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}