Chain Recurrence Classes of Generic Diffeomorphisms - Lecture 1B

Explore chain recurrence classes of generic diffeomorphisms in this mathematics lecture from the Simons Semester on Dynamics series. Delve into Conley's theory of Lyapunov functions separation of chain recurrence classes and examine examples of robustly non-hyperbolic diffeomorphisms. Learn about the C∞-generic coexistence of uncountably many chain recurrence classes without periodic orbit (aperiodic classes) functioning as adding machines. Discover properties of chain recurrence classes containing periodic points and their relationships with homoclinic classes. Investigate recent findings on C^1-locally generic coexistence of uncountably many aperiodic classes that are not adding machines, including expansive, non-uniquely ergodic, non-minimal but transitive, and non-transitive but possibly uniquely ergodic cases. Master key concepts such as viral chain property of chain recurrence classes, flexible periodic points, and filtrating Markov partitions while understanding how these elements contribute to the generic coexistence of diverse aperiodic classes.