Metric and Ergodic Properties of Partially Hyperbolic Diffeomorphisms with Topological Neutral Center

Explore the metric and ergodic properties of partially hyperbolic diffeomorphisms with topological neutral center in this 56-minute lecture from the Simons Semester on Dynamics. Delve into the theory of partially hyperbolic maps, focusing on a class where the central direction exhibits controlled behavior. Examine the dichotomy between atomicity of the center direction and the Bernoulli property, and investigate the invariance principle for ergodic invariant measures. Learn about recent developments in this field, including the study of one-dimensional center directions and their implications for the dynamics of these systems.