  In the present paper we give a positive answer to a question posed by Viana
on the existence of positive Lyapunov exponents for symplectic cocycles.
Actually, we prove that for an open and dense set of Holder symplectic cocycles
over a non-uniformly hyperbolic diffeomorphism there are non-zero Lyapunov
exponents with respect to any invariant ergodic measure with the local product
structure.
