Smooth Dynamics: Bernoulli and K Properties

This lecture by the instructor explores the Bernoulli and K properties in smooth dynamics, focusing on Bernoulli shifts, Bernoulli and K systems, smooth Bernoulli systems, equivalence of K and Bernoulli properties, and examples of smooth K non-Bernoulli systems. The lecture also delves into translations on semisimple Lie groups, isometric center, and the Bernoulli property for natural systems. Additionally, it discusses the Ornstein-Weiss reduction, consequences of exponential mixing, and poses intriguing questions related to the implications of K on Bernoulli, the nature of horocycle flows, and the relationship between growth on the center and mixing properties.