Modified Schmidt games and Diophantine approximation with weights

Dmitry Kleinbock; Barak Weiss

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arXiv · 0805.2934

Modified Schmidt games and Diophantine approximation with weights

Dmitry Kleinbock·Barak Weiss

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Abstract

We show that the sets of weighted badly approximable vectors in $\Bbb R^n$ are winning sets of certain games, which are modifications of $(α,β)$-games introduced by W. Schmidt in 1966. The latter winning property is stable with respect to countable intersections, and is shown to imply full Hausdorff dimension.

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Dmitry Kleinbock, Barak Weiss. 2009-09-02. Modified Schmidt games and Diophantine approximation with weights. https://arxiv.org/abs/0805.2934

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