Some Arguments in Equidistribution - Lecture 8

Explore key concepts in equidistribution through this mathematics lecture from the Simons Semester on Dynamics series, where Professor Jon Chaika delves into measure preservation, ergodicity, and the Birkhoff ergodic theorem. Learn about the proof's application to continuous compactly supported functions and understand the ergodicity of irrational circle rotations. Examine Ratner/Masur's argument regarding ergodicity of flow on the 2-torus, followed by Codene's approach to similar concepts. Master the Hopf argument in relation to ergodicity and mixing of hyperbolic total automorphisms, and conclude with Dani's perspective on directional flow ergodicity in the 2-torus.