Equidistribution of expanding measures with local maximal dimension and Diophantine Approximation

Abstract

We 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.

arXiv comment27 pages

References in corpus (1)

• Equidistribution of expanding translates of curves and Dirichlet's theorem on Diophantine approximation

Cited by in corpus (2)

• Entropy and escape of mass for $SL(3,Z)\SL(3,R)$
• Entropy and Escape of Mass for Hilbert Modular Spaces