Seminários de Sistemas Dinâmicos.

We consider partially hyperbolic diffeomorphisms on compact manifolds. The phenomenon of Absolute Continuity of the central foliation, though interesting, is believed to be rare. If we focus our attention to diffeomorphisms with compact central leaves, there is an intuitive way to relate the phenomenon with central Lyapunov exponents. However, implementing this intuitive idea in practice proves difficult due to a lack of characterization of partially hyperbolic diffeomorphisms. There have been partial results for specific types of partially hyperbolic diffeomorphisms with compact central leaves. This talk is based on the paper Geometric expansion, Lyapunov exponents and foliations by Radu Saghin and Zhihong Xia which discusses a possible approach in cases where the central leaves are not necessarily compact. .