3:00–4:00 pm Eckhart 206
Title: Measure and Topological Rigidity beyond Homogeneous Dynamics
Abstract:
To study the asymptotic behavior of orbits of a dynamical system, one can look at orbit closures or invariant measures. When the underlying system has a homogeneous structure, usually coming from a Lie group, with appropriate assumptions a wide range of rigidity theorems show that ergodic invariant measures and orbit closures have to be well-behaved and can often be classified. I will describe joint work with Brown, Eskin, and Rodriguez Hertz, which establishes rigidity results for quite general smooth dynamical systems having some hyperbolicity. I will also explain some of the necessary assumptions as well as the homogeneous structures that emerge.