Time-Changes: Definitions, Basic Facts, Ergodicity and Mixing - Lecture 4

Time-Changes: Definitions, Basic Facts, Ergodicity and Mixing - Lecture 4

Explore the fourth lecture in a six-part series on horocycle flows and their time-changes, focusing on the fundamental definitions and properties of time-changes in dynamical systems. Delve into the mathematical concepts of ergodicity and mixing, examining how these properties manifest in time-changed flows. Learn about the relationship between original horocycle flows and their time-changed variants, understanding the preservation and modification of dynamical characteristics. Master key theoretical foundations that bridge the gap between classical horocycle flows and their perturbed versions, setting the stage for more advanced concepts like Ratner's Rigidity Theorem and applications beyond SL2(R).