Schmidt's game, Badly Approximable Linear Forms and Fractals
| dc.creator | Fishman, Lior | |
| dc.date | 2008-09-11 | |
| dc.date.accessioned | 2026-07-07T10:02:18Z | |
| dc.date.available | 2026-07-07T10:02:18Z | |
| dc.description | We 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.identifier | https://arxiv.org/abs/0809.2065 | |
| dc.identifier | http://arxiv.org/abs/0809.2065 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168924 | |
| dc.subject | Number Theory | |
| dc.title | Schmidt's game, Badly Approximable Linear Forms and Fractals | |
| dc.type | text |