Geodesic
Badly approximable vectors in affine subspaces: Jarn\'{\i}k-type result
Čebyševskij sbornik, Tome 12 (2011) no. 2, pp. 77-84

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Consider irrational affine subspace $ A\subset \mathbb{R}^d$ of dimension $a$. We prove that the set $$ \{\xi =(\xi_1,...,\xi_d) \in { A}:\quad q^{1/a}\cdot \max_{1\le i \le d} ||q\xi_i|| \to \infty,\quad q\to \infty\} $$ is an $\alpha$-winning set for every $\alpha \in (0,1/2]$. 
@article{CHEB_2011_12_2_a9,
     author = {Nikolay Moshchevitin},
     title = {Badly approximable vectors in affine subspaces: {Jarn\'{\i}k-type} result},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {77--84},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2011_12_2_a9/}
}
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Nikolay Moshchevitin. Badly approximable vectors in affine subspaces: Jarn\'{\i}k-type result. Čebyševskij sbornik, Tome 12 (2011) no. 2, pp. 77-84. http://geodesic.mathdoc.fr/item/CHEB_2011_12_2_a9/