Chain Recurrence Classes of Generic Diffeomorphisms - Lecture 3B

Explore a 33-minute lecture from the Simons Semester on Dynamics series focusing on chain recurrence classes of generic diffeomorphisms. Delve into advanced mathematical concepts including the notion of "viral" chain properties of chain recurrence classes, flexible periodic points, and filtrating Markov partitions. Learn how these tools contribute to understanding the C^1-locally generic coexistence of uncountably many aperiodic classes that are not adding machines, which can be expansive, non-uniquely ergodic, non-minimal but transitive, or non-transitive but possibly uniquely ergodic. Build upon previous discussions of Conley's theory of Lyapunov functions, robustly non-hyperbolic diffeomorphisms, and the properties of chain recurrence classes containing periodic points.