{
  "id": "1003.5321",
  "version": "v3",
  "published": "2010-03-27T21:06:25.000Z",
  "updated": "2011-12-20T12:55:52.000Z",
  "title": "Dynamics of tuples of matrices in Jordan form",
  "authors": [
    "George Costakis",
    "Ioannis Parissis"
  ],
  "comment": "28 pages, final version; incorporates the corrections and improvements of the anonymous referee. Numbering has changed, all paragraph counters after the first are increased by +1. Several typos corrected. Lemma 4.7 and Corollary 4.10 now have detailed proofs. The proof of Lemma 6.4 has been rewritten for clarity. To appear in Oper. Matrices",
  "journal": "Oper. Matrices 7 (2013), no. 1, 131--157",
  "categories": [
    "math.FA",
    "math.DS"
  ],
  "abstract": "A tuple (T_1,...,T_k) of (n x n) matrices over R is called hypercyclic if for some x in R^n the set {T^{m_1} T^{m_2}...T^{m_k} x : m_1,m_2,...,m_k in N} is dense in R^n. We prove that the minimum number of (n x n) matrices in Jordan form over R which form a hypercyclic tuple is n+1. This answers a question of Costakis, Hadjiloucas and Manoussos.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-12-20T12:55:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47A16",
      "11J72",
      "15A21"
    ],
    "keywords": [
      "jordan form",
      "minimum number",
      "hypercyclic tuple",
      "hadjiloucas"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.5321C"
    }
  }
}