{
  "id": "1611.06470",
  "version": "v1",
  "published": "2016-11-20T05:01:47.000Z",
  "updated": "2016-11-20T05:01:47.000Z",
  "title": "Bounded orbits of Diagonalizable Flows on finite volume quotients of products of $SL_2(\\mathbb{R})$",
  "authors": [
    "Jinpeng An",
    "Anish Ghosh",
    "Lifan Guan"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1605.08510",
  "categories": [
    "math.DS",
    "math.NT"
  ],
  "abstract": "We prove a number field analogue of W. M. Schmidt's conjecture on the intersection of weighted badly approximable vectors and use this to prove an instance of a conjecture of An, Guan and Kleinbock. Namely, let $G := SL_2(\\mathbb{R}) \\times \\dots \\times SL_2(\\mathbb{R}) $ and $\\Gamma$ be a lattice in $G$. We show that the set of points on $G/\\Gamma$ whose forward orbits under a one parameter Ad-semisimple subsemigroup of $G$ are bounded, form a hyperplane absolute winning set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-20T05:01:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite volume quotients",
      "diagonalizable flows",
      "bounded orbits",
      "hyperplane absolute winning set",
      "parameter ad-semisimple subsemigroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}