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arXiv · 1211.3019

Amount of failure of upper-semicontinuity of entropy in noncompact rank one situations, and Hausdorff dimension

Shirali Kadyrov·Anke D. Pohl
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Abstract

Recently, Einsiedler and the authors provided a bound in terms of escape of mass for the amount by which upper-semicontinuity for metric entropy fails for diagonal flows on homogeneous spaces $Γ\backslash G$, where $G$ is any connected semisimple Lie group of real rank 1 with finite center and $Γ$ is any nonuniform lattice in $G$. We show that this bound is sharp and apply the methods used to establish bounds for the Hausdorff dimension of the set of points which diverge on average.

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Shirali Kadyrov, Anke D. Pohl. 2012-11-13. Amount of failure of upper-semicontinuity of entropy in noncompact rank one situations, and Hausdorff dimension. https://arxiv.org/abs/1211.3019

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