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

Hao Xing

Published 2022-12-29Version 1

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.