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arXiv · 1102.4431

Badly approximable vectors in affine subspaces: Jarn\'{\i}k-type result

Nikolay Moshchevitin
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Abstract

Consider irrational affine subspace $ A\subset \mathbb{R}^d$ of dimension $a$. We prove that the set $$ \{\xi =(\xi_1,...,\xi_d) \in {A}:\,\,\, \ q^{1/a}\cdot \max_{1\le i \le d} ||q\xi_i|| \to \infty,\,\,\,\, q\to \infty\} $$ is an $\alpha$-winning set for every $\alpha \in (0,1/2]$

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Nikolay Moshchevitin. 2011-02-22. Badly approximable vectors in affine subspaces: Jarn\'{\i}k-type result. https://arxiv.org/abs/1102.4431

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