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Watch a 56-minute mathematics lecture from the Simons Semester on Dynamics series exploring equidistribution arguments and ergodic theory fundamentals. Delve into measure preservation, ergodicity definitions, and the Birkhoff ergodic theorem, including its proof and applications to continuous compactly supported functions. Examine the ergodicity of irrational circle rotations and flows on the 2-torus through various mathematical arguments, including approaches by Ratner/Masur, Codene, and Dani. Study the ergodicity and mixing properties of hyperbolic total automorphisms using the Hopf argument, while building understanding through carefully constructed examples and proofs.
