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arXiv · 1110.0910

Escape of mass and entropy for diagonal flows in real rank one situations

Manfred Einsiedler·Shirali Kadyrov·Anke Pohl
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Abstract

Let $G$ be a connected semisimple Lie group of real rank 1 with finite center, let $Γ$ be a non-uniform lattice in $G$ and $a$ any diagonalizable element in $G$. We investigate the relation between the metric entropy of $a$ acting on the homogeneous space $Γ\backslash G$ and escape of mass. Moreover, we provide bounds on the escaping mass and, as an application, we show that the Hausdorff dimension of the set of orbits (under iteration of $a$) which miss a fixed open set is not full.

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Manfred Einsiedler, Shirali Kadyrov, Anke Pohl. 2014-09-09. Escape of mass and entropy for diagonal flows in real rank one situations. https://arxiv.org/abs/1110.0910

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