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Explore chain recurrence classes and their properties in this 35-minute 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) that function as adding machines. Discover the relationships between chain recurrence classes containing periodic points and their homoclinic classes, while gaining insights into recent mathematical developments including viral chain properties, flexible periodic points, and filtrating Markov partitions. Understand how these concepts contribute to the C^1-locally generic coexistence of uncountably many aperiodic classes with diverse dynamical behaviors.
