{
  "id": "1501.05409",
  "version": "v1",
  "published": "2015-01-22T07:22:05.000Z",
  "updated": "2015-01-22T07:22:05.000Z",
  "title": "Bounded orbits of diagonalizable flows on $\\rm{SL}_3(\\mathbb{R})/\\rm{SL}_3(\\mathbb{Z})$",
  "authors": [
    "Jinpeng An",
    "Lifan Guan",
    "Dmitry Kleinbock"
  ],
  "comment": "20 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove that for any countably many one-parameter diagonalizable subgroups $F_n$ of $\\rm{SL}_3(\\mathbb{R})$, the set of $\\Lambda\\in\\rm{SL}_3(\\mathbb{R})/\\rm{SL}_3(\\mathbb{Z})$ such that all the orbits $F_n\\Lambda$ are bounded has full Hausdorff dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-22T07:22:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A17",
      "11J13"
    ],
    "keywords": [
      "diagonalizable flows",
      "bounded orbits",
      "full hausdorff dimension",
      "one-parameter diagonalizable subgroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150105409A"
    }
  }
}