{
  "id": "0905.1152",
  "version": "v2",
  "published": "2009-05-08T00:43:44.000Z",
  "updated": "2009-05-11T17:33:21.000Z",
  "title": "Equidistribution of expanding measures with local maximal dimension and Diophantine Approximation",
  "authors": [
    "Ronggang Shi"
  ],
  "comment": "27 pages",
  "categories": [
    "math.DS",
    "math.NT"
  ],
  "abstract": "We consider improvements of Dirichlet's Theorem on space of matrices $M_{m,n}(R)$. It is shown that for a certain class of fractals $K\\subset [0,1]^{mn}\\subset M_{m,n}(R)$ of local maximal dimension Dirichlet's Theorem cannot be improved almost everywhere. This is shown using entropy and dynamics on homogeneous spaces of Lie groups.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-05-11T17:33:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E40",
      "28D20",
      "11J83"
    ],
    "keywords": [
      "diophantine approximation",
      "expanding measures",
      "local maximal dimension dirichlets theorem",
      "equidistribution",
      "lie groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.1152S"
    }
  }
}