Equidistribution of expanding measures with local maximal dimension and Diophantine Approximation

2009/05/08 by Ronggang Shi, Shi, Ronggang · 2 citations
Mathematics · #11J83 (Secondary) #22E40 (Primary) 28D20 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Stochastic processes and statistical mechanics #advanced mathematical theories #math.DS #math.NT #msc:11J83 #msc:22E40 #msc:28D20

paper · pdf · doi:10.48550/arxiv.0905.1152

27 pages

openalex publication_date 2009/05/08 · arxiv created 2009/05/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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⊂ [0,1]^mn⊂ 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.

Cited by

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

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