Hyperbolic dynamical systems, invariant geometric structures, and rigidity
type: Item
instance of: scholarly article
title: Hyperbolic dynamical systems, invariant geometric structures, and rigidity
zbMATH Open document ID: 0831.58039
author: Renato Feres
published in: Mathematical Research Letters
publication date: 1996-02-13T00:00:00Z
review text: This paper provides a brief survey of the field of geometric rigidity, an area related to both differential geometry and to the theory of hyperbolic dynamical systems. The concept of rigidity is a property that certain classes of group actions possess that permit them to be classified, using a suitable notion of equivalence, by a small number of algebraically-defined model actions. For the most part, these model actions are given as automorphisms of double coset spaces of the form \(\Gamma \setminus G/H\) where \(H\) is a closed subgroup of the Lie group \(G\), and \(\Gamma\) is a discrete subgroup. Important examples of rigidity theories include Gromov's theory of rigid transformation groups, Zimmer's surperrigidity theory for cocycles of actions of higher rank, semisimple Lie groups and lattices, and Katok and Spatzier's study of abelian Anosov actions.
Mathematics Subject Classification ID: 37D99
Mathematics Subject Classification ID: 22E40
zbMATH DE Number: 794207
zbMATH Keywords: rigidity
zbMATH Keywords: rigid geometric structure
zbMATH Keywords: invariant geometric structures
zbMATH Keywords: hyperbolic dynamical systems
reviewed by: William J. Satzer Jr.
MaRDI profile type: Publication
full work available at URL: mrl.1994.v1.n1.a2
OpenAlex ID: W2066230787
DOI: 10.4310/MRL.1994.V1.N1.A2
description: scientific article; zbMATH DE number 794207