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Equidistribution of expanding measures with local maximal dimension and Diophantine Approximation

by Shi, Ronggang

Abstract (Summary)
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 $Ksubset [0,1]^{mn}subset M_{m,n}(R)$ 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.
Bibliographical Information:

Advisor:

School:The Ohio State University

School Location:USA - Ohio

Source Type:Master's Thesis

Keywords:ergodic theory entropy dirichlet s theorem

ISBN:

Date of Publication:07/14/2009

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