{
  "id": "2212.14436",
  "version": "v1",
  "published": "2022-12-29T19:20:17.000Z",
  "updated": "2022-12-29T19:20:17.000Z",
  "title": "Fractional dimension related to badly approximable matrices associated with higher successive minima",
  "authors": [
    "Hao Xing"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1901.06602 by other authors",
  "categories": [
    "math.NT",
    "math.CA"
  ],
  "abstract": "In this article we introduce the notion of badly approximable matrices of higher order using higher sucessive minima in $\\mathbb R^d$. We prove that for order less than $d$, they have Lebesgue measure zero and the gaps between them still have full Hausdorff dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-29T19:20:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "badly approximable matrices",
      "higher successive minima",
      "fractional dimension",
      "full hausdorff dimension",
      "lebesgue measure zero"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}