Chain Recurrence Classes of Generic Diffeomorphisms - Lecture 2B

Explore chain recurrence classes and their properties in this 34-minute mathematics lecture from the Simons Semester on Dynamics series. Delve into Conley's theory of Lyapunov functions separation and examine examples of robustly non-hyperbolic diffeomorphisms that lead to C∞-generic coexistence of uncountably many chain recurrence classes without periodic orbit (aperiodic classes). Learn about the properties of chain recurrence classes containing periodic points and their relationships with homoclinic classes. Discover recent research findings on C^1-locally generic coexistence of uncountably many aperiodic classes that are not adding machines, including expansive, non-uniquely ergodic, and non-transitive 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 dynamical behaviors in aperiodic classes.