Boundaries, rigidity of representations, and Lyapunov exponents

TL;DR

This paper explores the relationship between measurable dynamics, group boundaries, and rigidity, introducing a new ergodic feature to establish rigidity results and demonstrate the simplicity of Lyapunov exponents in certain systems.

Contribution

It introduces a novel ergodic property of group boundaries and applies it to prove rigidity of representations and simplicity of Lyapunov exponents.

Findings

New ergodic feature of group boundaries identified

Rigidity results for group representations established

Simplicity of Lyapunov exponents proven for specific systems

Abstract

In this paper we discuss some connections between measurable dynamics and rigidity aspects of group representations and group actions. A new ergodic feature of familiar group boundaries is introduced, and is used to obtain rigidity results for group representations and to prove simplicity of Lyapunov exponents for some dynamical systems.