Measure Rigidity beyond Homogeneous Dynamics

TL;DR

This paper extends measure and topological rigidity results from homogeneous Lie group actions to more general manifolds, broadening the scope of dynamical systems theory.

Contribution

It introduces new methods to generalize rigidity phenomena beyond homogeneous spaces to arbitrary manifolds.

Findings

Rigidity results now apply to a wider class of manifolds.

New techniques developed for non-homogeneous dynamical systems.

Enhanced understanding of measure and topological properties in complex manifolds.

Abstract

We describe recent work that extends some of the measure and topological rigidity results in dynamical systems from situations homogeneous under a Lie group to quite general manifolds.