Positive Lyapunov exponents for symplectic cocycles

Abstract

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.

This paper has been withdrawn by the authors due to the incomplete argument when dealing with the "generic center" in Lemma 4.6. This argument is completed in a new paper by the authors together with Jairo Bochi, Michel Cambrainha, Carlos Matheus and Disheng Xu