Non-hyperbolic Measures of Maximally Possible Entropy in Transitive Dynamical Systems

Explore the intricacies of non-hyperbolic measures in transitive nonhyperbolic partially hyperbolic diffeomorphisms in this 52-minute lecture by Katrin Gelfert from the Federal University of Rio de Janeiro. Delve into the quantification of "lack of hyperbolicity" through the study of skew products of C^1 circle diffeomorphisms, which exemplify nonhyperbolic behavior in robustly transitive dynamical systems. Examine how these models arise from projective actions of certain 2x2 elliptic matrix cocycles and their relevance to C^1 partially hyperbolic diffeomorphisms with one-dimensional center bundles. Investigate the coexistence of saddles with different hyperbolicity types, described through fiber-expanding and -contracting regions intermingled by dynamics. Analyze nonhyperbolic ergodic measures characterized by zero Lyapunov exponents in the circle fiber direction. Engage with a multifractal analysis of fiber-Lyapunov exponents and discover restricted variational principles relating topological entropy of level sets to metric entropy of ergodic measures. Learn about the construction of ergodic nonhyperbolic measures with maximal possible entropy, based on joint work with L.J. Díaz, M. Rams, B. Santiago, and J. Zhang.

Katrin Gelfert (Federal University of Rio de Janeiro)