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arXiv · 1411.0803

Exceptional sets in homogeneous spaces and Hausdorff dimension

Shirali Kadyrov
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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 $$\dim X + C\frac{r^{\dim X}}{\log r},$$ 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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Shirali Kadyrov. 2014-11-04. Exceptional sets in homogeneous spaces and Hausdorff dimension. https://arxiv.org/abs/1411.0803

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