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

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

2011-10-05

arxiv.org/abs/1110.0910v1

Mathematics

Dynamical Systems

24 pages, 2 figures

Scientific paper

Let $G$ be any connected semisimple Lie group of real rank 1 with finite
center, let $\Gamma$ be any 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 $\Gamma\backslash G$ and escape
of mass. Moreover, we provide bounds on the escaping mass.

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