{
  "id": "1407.8343",
  "version": "v2",
  "published": "2014-07-31T10:19:54.000Z",
  "updated": "2014-11-27T08:46:02.000Z",
  "title": "Direct topological factorization for topological flows",
  "authors": [
    "Tom Meyerovitch"
  ],
  "comment": "21 pages. The previous contained a false proof for the claim that any expansive flow admits a direct topological factorization into direct-prime systems",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the notion of \\emph{direct factorization} for topological dynamical systems. This notion was considered the early 1980's by D. Lind for $\\mathbb{Z}$-shifts of finite type. Here we consider more general situations, where the acting group $\\mathbb{G}$ is countable but not necessarily equal to $\\mathbb{Z}$. Also, we consider situations where the system is not a subshift of finite type. Direct factorizations for $\\mathbb{G}$-shifts of finite type are considered, in particular when $\\mathbb{G}=\\mathbb{Z}^d$. We study direct factorizations for specific systems, and prove that the \"$3$-colored-chessboard\" and certain Dyck shifts are topologically direct-prime.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-31T10:19:54.000Z",
      "abstract": "We study the notion of \\emph{direct factorization} for topological flows, focusing on symbolic systems. This notion was considered the early 1980's by D. Lind for $\\mathbb{Z}$-shifts of finite type. It turns out that any expansive flow admits a \"direct prime factorization\". Direct factorizations for $\\mathbb{Z}^d$-shifts of finite type are considered. We prove that the \"$3$-colored-chessboard\" and certain Dyck shifts are topologically direct-prime.",
      "comment": "19 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-11-27T08:46:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "37B10",
      "37B50",
      "37B40"
    ],
    "keywords": [
      "direct topological factorization",
      "topological flows",
      "finite type",
      "direct prime factorization",
      "symbolic systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.8343M"
    }
  }
}