Watch a 52-minute mathematics lecture from the Simons Semester on Dynamics series where Professor Christian Bonatti explores chain recurrence classes of generic diffeomorphisms. Delve into Conley's theory of Lyapunov functions separation, examining examples of robustly non-hyperbolic diffeomorphisms and their relationship to chain recurrence classes without periodic orbits. Learn about properties of chain recurrence classes containing periodic points and their connections to homoclinic classes. Discover recent research findings on C^1-locally generic coexistence of uncountably many aperiodic classes, exploring key concepts like viral chain properties, flexible periodic points, and filtrating Markov partitions. Understand how these elements combine to demonstrate the generic coexistence of numerous aperiodic classes exhibiting diverse dynamical behaviors, from expansive and non-uniquely ergodic to non-minimal but transitive systems.