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arXiv · 2212.14436

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

Hao Xing
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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.

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Hao Xing. 2022-12-29. Fractional dimension related to badly approximable matrices associated with higher successive minima. https://arxiv.org/abs/2212.14436

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