Some Arguments in Equidistribution - Lecture 2

Watch a 54-minute mathematics lecture exploring equidistribution arguments and ergodic theory, delivered by Jon Chaika from the University of Utah as part of the Simons Semester on Dynamics. Delve into measure preservation and ergodicity concepts, examining the Birkhoff ergodic theorem and its applications to continuous compactly supported functions. Study the ergodicity of irrational circle rotations and flows on the 2-torus through various mathematical arguments, including approaches by Ratner/Masur, Codene, and Dani. Explore the ergodicity and mixing properties of hyperbolic total automorphisms using the Hopf argument, building a comprehensive understanding of these fundamental concepts in dynamical systems.