Fractional dimension related to badly approximable matrices associated with higher successive minima

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.

arXiv admin note: text overlap with arXiv:1901.06602 by other authors