Hyperbolic dynamical systems, invariant geometric structures, and rigidity
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.
scientific article; zbMATH DE number 794207