2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/229747We consider improvements of Dirichlet's Theorem on space of matrices $M_{m,n}(R)$. It is shown that for a certain class of fractals $K\subset [0,1]^{mn}\subset M_{m,n}(R)$ of local maximal dimension Dirichlet's Theorem cannot be improved almost everywhere. This is shown using entropy and dynamics on homogeneous spaces of Lie groups.27 pagesDynamical SystemsNumber Theory22E40 (Primary) 28D20, 11J83 (Secondary)text