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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2022
- DOI:
- 10.48550/arXiv.2212.14436
- arXiv:
- arXiv:2212.14436
- Bibcode:
- 2022arXiv221214436X
- Keywords:
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- Mathematics - Number Theory;
- Mathematics - Classical Analysis and ODEs
- E-Print:
- arXiv admin note: text overlap with arXiv:1901.06602 by other authors