Schmidt's game, Badly Approximable Linear Forms and Fractals

dc.creatorFishman, Lior
dc.date2008-09-11
dc.date.accessioned2026-07-07T10:02:18Z
dc.date.available2026-07-07T10:02:18Z
dc.descriptionWe prove that for every two natural numbers M and N, if Tau is a Borel, finite, absolutely friendly measure on a compact set K of R^MN, then the intersection of K and 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\times 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 R^(M\times N) satisfying the open set condition, (the Cantor ternary set, Koch's curve and Sierpinski's gasket to name a few examples), the dimK=dimK\capBA(M,N).
dc.identifierhttps://arxiv.org/abs/0809.2065
dc.identifierhttp://arxiv.org/abs/0809.2065
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168924
dc.subjectNumber Theory
dc.titleSchmidt's game, Badly Approximable Linear Forms and Fractals
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