{
  "id": "2001.09539",
  "version": "v1",
  "published": "2020-01-26T23:44:38.000Z",
  "updated": "2020-01-26T23:44:38.000Z",
  "title": "The G^0-periodic points of a linear system",
  "authors": [
    "Victor Ayala",
    "Adriano Da Silva"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper we show that the compactness of the central subgroup $G^0$ associated with the drift of a linear system $\\Sigma_G$ on a connected Lie group $G$ is a necessary and sufficient condition for the boundedness of the $G^0$-periodic points of $\\Sigma_G$. As a consequence, the control set containing the identity element of $G$ is bounded if and only if $G^0$ is a compact subgroup.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-26T23:44:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "linear system",
      "identity element",
      "control set",
      "periodic points",
      "central subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}