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Equidistribution of expanding measures with local maximal dimension and diophantine approximation

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Abstract

We consider improvements of Dirichlet’s Theorem on the space of matrices \({M_{m,n}(\mathbb R)}\). It is shown that for a certain class of fractals \({K\subset [0,1]^{mn}\subset M_{m,n}(\mathbb R)}\) 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.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, People’s Republic of China

    Ronggang Shi

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  1. Ronggang Shi
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Correspondence to Ronggang Shi.

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Communicated by S. G. Dani.

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Shi, R. Equidistribution of expanding measures with local maximal dimension and diophantine approximation. Monatsh Math 165, 513–541 (2012). https://doi.org/10.1007/s00605-011-0300-x

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  • DOI: https://doi.org/10.1007/s00605-011-0300-x

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