TY - JOUR
T1 - Modified Schmidt games and Diophantine approximation with weights
AU - Kleinbock, Dmitry
AU - Weiss, Barak
N1 - Funding Information:
The authors are grateful to the hospitality of Tata Institute of Fundamental Research (Mumbai) where they had several conversations which eventually led to results described in this paper. Thanks are also due to Elon Lindenstrauss for motivating discussions, to the referee for useful comments, and to Max Planck Institute for Mathematics (Bonn) where the paper was completed. This work was supported by BSF grant 2000247, ISF grant 584/04, and NSF grants DMS-0239463, DMS-0801064.
PY - 2010/3/1
Y1 - 2010/3/1
N2 - We show that the sets of weighted badly approximable vectors in Rn are winning sets of certain games, which are modifications of (α, β)-games introduced by W.M. Schmidt in 1966. The latter winning property is stable with respect to countable intersections, and is shown to imply full Hausdorff dimension.
AB - We show that the sets of weighted badly approximable vectors in Rn are winning sets of certain games, which are modifications of (α, β)-games introduced by W.M. Schmidt in 1966. The latter winning property is stable with respect to countable intersections, and is shown to imply full Hausdorff dimension.
KW - Badly approximable vectors
KW - Diophantine approximation
KW - Hausdorff dimension
KW - Schmidt's game
UR - https://www.scopus.com/pages/publications/73749083401
U2 - 10.1016/j.aim.2009.09.018
DO - 10.1016/j.aim.2009.09.018
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AN - SCOPUS:73749083401
SN - 0001-8708
VL - 223
SP - 1276
EP - 1298
JO - Advances in Mathematics
JF - Advances in Mathematics
IS - 4
ER -