Two-dimensional badly approximable vectors and Schmidt's game

By Jinpeng An. 2012

49 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/53b87563afd405ab721334840a9a1d17e1a0221c

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In Computational Theory and Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Metric Diophantine Approximation : aspects of recent work (2016, background): “ higher dimensions (n>2), removing condition (7.17) remains very much a key open problem. The recent work of Guan and Yu [43] makes a contribution toward this problem. Building upon the work of An [2], they show that the set Bad(i 1,...,in) is winning whenever i 1 = ··· = in−1 ≥ in. So far we hav”