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arXiv · 2310.00122

Dimension bounds for escape on average in homogeneous spaces

Dmitry Kleinbock·Shahriar Mirzadeh
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Abstract

Let $X = G/\Gamma$, where $G$ is a Lie group and $\Gamma$ is a uniform lattice in $G$, and let $O$ be an open subset of $X$. We give an upper estimate for the Hausdorff dimension of the set of points whose trajectories escape $O$ on average with frequency $\delta$, where $0 < \delta \le 1$.

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Dmitry Kleinbock, Shahriar Mirzadeh. 2023-09-29. Dimension bounds for escape on average in homogeneous spaces. https://arxiv.org/abs/2310.00122

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