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

M. Einsiedler, S. Kadyrov, A. Pohl

Research output: Contribution to journalArticle

5 Citations (Scopus)

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\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.

Original languageEnglish
Pages (from-to)245-295
Number of pages51
JournalIsrael Journal of Mathematics
Volume210
Issue number1
DOIs
Publication statusPublished - Sep 1 2015
Externally publishedYes

Fingerprint

Entropy
Metric Entropy
Semisimple Lie Group
Homogeneous Space
Hausdorff Dimension
Open set
Orbit
Iteration

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Escape of mass and entropy for diagonal flows in real rank one situations. / Einsiedler, M.; Kadyrov, S.; Pohl, A.

In: Israel Journal of Mathematics, Vol. 210, No. 1, 01.09.2015, p. 245-295.

Research output: Contribution to journalArticle

Einsiedler, M. ; Kadyrov, S. ; Pohl, A. / Escape of mass and entropy for diagonal flows in real rank one situations. In: Israel Journal of Mathematics. 2015 ; Vol. 210, No. 1. pp. 245-295.
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