{
  "id": "2103.13152",
  "version": "v1",
  "published": "2021-03-24T12:53:12.000Z",
  "updated": "2021-03-24T12:53:12.000Z",
  "title": "Common hypercyclic vectors and dimension of the parameter set",
  "authors": [
    "Frédéric Bayart",
    "Fernando Costa",
    "Quentin Menet"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We investigate the existence of a common hypercyclic vector for a family $(T_\\lambda)_{\\lambda\\in \\Lambda}$ of hypercyclicoperators acting on the same Banach space $X$. We give positive and negative results involving the dimension of $\\Lambda$ and the regularity of each map $\\lambda\\in \\Lambda\\mapsto T_\\lambda^n x$, $x\\in X$, $n\\in\\mathbb N$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-24T12:53:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "common hypercyclic vector",
      "parameter set",
      "banach space",
      "hypercyclicoperators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}