Stably positive Lyapunov exponents for symplectic linear cocycles over   partially hyperbolic diffeomorphisms
  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 H\"older topology. 
Mauricio Poletti
math.DS