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- W2048120416 abstract "We prove that for every M,N∈N, if τ is a Borel, finite, absolutely friendly measure supported on a compact subset K of RMN, then K∩BA(M,N) is a winning set in Schmidt's game sense played on K, where BA(M,N) is the set of badly approximable M×N matrices. As an immediate consequence we have the following application. If K is the attractor of an irreducible finite family of contracting similarity maps of RMN satisfying the open set condition (the Cantor's ternary set, Koch's curve and Sierpinski's gasket to name a few known examples), thendimK=dimK∩BA(M,N)." @default.
- W2048120416 created "2016-06-24" @default.
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- W2048120416 date "2009-09-01" @default.
- W2048120416 modified "2023-09-23" @default.
- W2048120416 title "Schmidt's game, badly approximable matrices and fractals" @default.
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- W2048120416 doi "https://doi.org/10.1016/j.jnt.2009.02.005" @default.
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