{
  "id": "1512.01266",
  "version": "v1",
  "published": "2015-12-03T22:13:08.000Z",
  "updated": "2015-12-03T22:13:08.000Z",
  "title": "Some universality results for dynamical systems",
  "authors": [
    "Udayan B. Darji",
    "Étienne Matheron"
  ],
  "comment": "15 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove some \"universality\" results for topological dynamical systems. In particular, we show that for any continuous self-map $T$ of a perfect Polish space, one can find a dense, $T$-invariant set homeomorphic to the Baire space ${\\mathbb N}^{\\mathbb N}$; that there exists a bounded linear operator $U: \\ell_1 \\rightarrow \\ell_1$ such that any linear operator $T$ from a separable Banach space into itself with $\\Vert T\\Vert\\leq 1$ is a linear factor of $U$; and that given any $\\sigma$-compact family ${\\mathcal F}$ of continuous self-maps of a compact metric space, there is a continuous self-map $U_{\\mathcal F}$ of ${\\mathbb N}^{\\mathbb N}$ such that each $T\\in {\\mathcal F}$ is a factor of $U_{\\mathcal F}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-03T22:13:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B99",
      "54H20",
      "54C20",
      "47A99"
    ],
    "keywords": [
      "dynamical systems",
      "universality results",
      "continuous self-map",
      "compact metric space",
      "invariant set homeomorphic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}