Stably positive Lyapunov exponents for symplectic linear cocycles over partially hyperbolic diffeomorphisms

Abstract

We consider symplectic cocycles over two classes of partially hyperbolic diffeomorphisms: having compact center leaves and time one maps of Anosov flows. We prove that the Lyapunov exponents are non-zero in an open and dense set in the Hölder topology.

To appear in Discrete and Continuous Dynamical Systems