{
  "id": "math/0506510",
  "version": "v1",
  "published": "2005-06-24T19:11:58.000Z",
  "updated": "2005-06-24T19:11:58.000Z",
  "title": "Flows on $S$-arithmetic homogeneous spaces and applications to metric Diophantine approximation",
  "authors": [
    "Dmitry Kleinbock",
    "George Tomanov"
  ],
  "comment": "56 pages; an earlier version is available as an MPI (Bonn) preprint, 2003",
  "categories": [
    "math.NT",
    "math.DS"
  ],
  "abstract": "The main goal of this work is to establish quantitative nondivergence estimates for flows on homogeneous spaces of products of real and $p$-adic Lie groups. These results have applications both to ergodic theory and to Diophantine approximation. Namely, earlier results of Dani (finiteness of locally finite ergodic unipotent-invariant measures on real homogeneous spaces) and Kleinbock-Margulis (strong extremality of nondegenerate submanifolds of $\\Bbb R^n$) are generalized to the $S$-arithmetic setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-06-24T19:11:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J83",
      "37A13"
    ],
    "keywords": [
      "metric diophantine approximation",
      "arithmetic homogeneous spaces",
      "applications",
      "locally finite ergodic unipotent-invariant measures",
      "adic lie groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 56,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......6510K"
    }
  }
}