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Watch a 48-minute lecture exploring the evolution and significance of partially hyperbolic dynamics in mathematical systems. Delve into the historical development of hyperbolic dynamical systems, introduced by Smale, Anosov, and Sinai in the 1960s, and understand their original goals of characterizing stable systems and establishing a framework for general dynamical behavior. Learn how the concept of partial hyperbolicity emerged as a crucial generalization when the initial hyperbolicity paradigm proved too restrictive. Examine the distinctive characteristics of partially hyperbolic systems, with particular focus on their rigidity properties, Lyapunov exponents, and the occurrence of pathological foliations, as presented by renowned mathematician Marcelo Viana da Silva from IMPA, Brazil.
