Exceptional sets in homogeneous spaces and Hausdorff dimension
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Date
2015
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Publisher
Dynamical Systems An International Journal
Abstract
In this paper, we study the dimension of a family of sets arising in open dynamics. We use exponential mixing results for diagonalizable flows in compact homogeneous spaces X to show that the Hausdorff dimension of set of points that lie on trajectories missing a particular open ball of radius r is at most dim X + C rdim X log r , where C > 0 is a constant independent of r > 0. Meanwhile, we also describe a general method for computing the least cardinality of open covers of dynamical sets using volume estimates.
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Keywords
exponential mixing, homogeneous dynamics, Hausdorff dimension
Citation
Kadyrov Sh / Exceptional sets in homogeneous spaces and Hausdorff dimension / Dynamical Systems An International Journal / 2015