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

Autor:	Kadyrov, Shirali, Pohl, Anke D.
Rok vydání:	2012
Předmět:	Mathematics - Dynamical Systems Primary: 37A35 37D40 Secondary: 28D20 22D40
Druh dokumentu:	Working Paper
Popis:	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 $\Gamma\backslash G$, where $G$ is any connected semisimple Lie group of real rank 1 with finite center and $\Gamma$ 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. Comment: 24 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1211.3019 Zobrazit plný text záznamu View this record from Arxiv