Modified Schmidt games and Diophantine approximation with weights

Details Modified Schmidt games and Diophantine approximation with weights Modified Schmidt games and Diophantine approximation with weights

2008-05-19

arxiv.org/abs/0805.2934v2

Advances in Math. 223 (2010), 1276-1298

Mathematics

Number Theory

26 pages; a substantially revised version

Scientific paper

We show that the sets of weighted badly approximable vectors in $\Bbb R^n$
are winning sets of certain games, which are modifications of
$(\alpha,\beta)$-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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