Ergodic properties of discrete groups; inheritance to normal subgroups and invariance under quasiconformal deformations
type: Item
instance of: scholarly article
title: Ergodic properties of discrete groups; inheritance to normal subgroups and invariance under quasiconformal deformations
zbMATH Open document ID: 0782.30037
author: Katsuhiko Matsuzaki
published in: Journal of Mathematics of Kyoto University
publication date: 1993-09-16T00:00:00Z
review text: The author gives some results concerning ergodic properties of isometry groups \(\Gamma\) acting on the \(n\)-dimensional hyperbolic space \(B^ n=\{x\in\mathbb{R}^ n\bigl|\) \(| x|<1\}\) and on the sphere \(S^{n-1}\). These results are in connection with those obtained by \textit{T. Lyons} and \textit{D. Sullivan} [J. Diff. Geom. 19, 299-323 (1984; Zbl 0554.58022)]. In the paper under review it is studied in what degree any normal subgroup of \(\Gamma\) inherits ergodicity on \(S^{n-1}\times S^{n-1}\) and on \(S^{n-1}\). In the case \(n=2\) it is proved that \(B^ 2/\Gamma\) is recurrent iff any nontrivial normal subgroup of \(\Gamma\) is conservative. It is studied whether the ergodic properties on \(S^{n-1}\) are preserved or not by deformations of \(\Gamma\) under quasi-isometric automorphisms of \(B^ n\).
Mathematics Subject Classification ID: 30F99
Mathematics Subject Classification ID: 30F35
Mathematics Subject Classification ID: 37A99
Mathematics Subject Classification ID: 30C65
zbMATH DE Number: 408744
reviewed by: Emilia Petrisor
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250519345
OpenAlex ID: W1941293397
DOI: 10.1215/KJM/1250519345
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description: scientific article; zbMATH DE number 408744