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arXiv · 1204.3610

Two-dimensional badly approximable vectors and Schmidt's game

Jinpeng An
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Abstract

We prove that for any pair $(s,t)$ of nonnegative numbers with $s+t=1$, the set of two-dimensional $(s,t)$-badly approximable vectors is winning for Schmidt's game. As a consequence, we give a direct proof of Schmidt's conjecture using his game.

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Jinpeng An. 2012-04-16. Two-dimensional badly approximable vectors and Schmidt's game. https://doi.org/10.1215/00127094-3165862

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