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

2011/10/05 by Manfred Einsiedler, Einsiedler, Manfred, Shirali Kadyrov +3
Mathematics · #22D40 (Secondary) #37A35 (Primary) 28D20 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:22D40 #msc:28D20 #msc:37A35

paper · pdf · doi:10.48550/arxiv.1110.0910

40 pages, 1 figure

arxiv created 2014/09/09 · arxiv updated 2014/09/10

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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