Some Arguments in Equidistribution - Lecture 1

Watch a mathematics lecture exploring fundamental concepts in equidistribution theory and ergodic dynamics, delivered by Jon Chaika from the University of Utah as part of the Simons Semester on Dynamics. Delve into measure preservation and ergodicity definitions, examine the Birkhoff ergodic theorem and its implications for continuous compactly supported functions, and understand its converse. Learn about the ergodicity of irrational circle rotations, explore Ratner/Masur's argument for ergodicity of flow on the 2-torus, and study Codene's approach to directional flows. Conclude with an investigation of hyperbolic total automorphisms through the Hopf argument and examine Dani's perspective on directional flows on the 2-torus. The 52-minute lecture provides a comprehensive foundation in equidistribution theory and its various applications in dynamical systems.