{
  "id": "1010.5915",
  "version": "v2",
  "published": "2010-10-28T10:49:18.000Z",
  "updated": "2021-01-26T07:10:54.000Z",
  "title": "Hypercyclic Abelian Semigroups of Matrices on $\\mathbb{R}^n$",
  "authors": [
    "Adlene Ayadi",
    "Habib Marzougui"
  ],
  "comment": "24 pages",
  "journal": "Topol. Appl. 210 (2016) 29--45]. Corrigendum: Topology Appl. 287 (2021), 107330",
  "doi": "10.1016/j.topol.2016.07.007 10.1016/j.topol.2020.107330",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we bring together results about the existence of a somewhere dense (resp. dense) orbit and the minimal number of generators for abelian semigroups of matrices on $\\mathbb{R}^n$. We solve the problem of determining the minimal number of matrices in normal form over $\\mathbb{R}$ which form a hypercyclic abelian semigroup on R^n. In particular, we show that no abelian semigroup generated by $[\\frac{n+1}{2}]$ matrices on $\\mathbb{R}^n$ can be hypercyclic. ([ ] denotes the integer part). This is a corrected version of the paper published in Topology and its Applications 210 (2016), 29-45 (see also [4]). The differences between this version and the published version are explained at the end of the Introduction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-10-28T10:49:18.000Z",
      "title": "Hypercyclic Abelian Semigroups of Matrices on Rn",
      "abstract": "We give a complete characterization of existence of dense orbit for any abelian semigroup of matrices on R^{n}. For finitely generated semigroups, this characterization is explicit and it is used to determine the minimal number of matrices in normal form over R which form a hypercyclic abelian semigroup on R^{n}. In particular, we show that no abelian semigroup generated by [(n+1)/2] matrices on Rn can be hyper-cyclic. ([ ] denotes the integer part).",
      "comment": "19 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2021-01-26T07:10:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C85",
      "47A16"
    ],
    "keywords": [
      "hypercyclic abelian semigroup",
      "dense orbit",
      "minimal number",
      "normal form",
      "complete characterization"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.5915A"
    }
  }
}