Lyapunov exponents of partially hyperbolic volume-preserving maps with 2-dimensional center bundle

We consider the set of partially hyperbolic symplectic diffeomorphisms which are accessible, have 2-dimensional center bundle and satisfy some pinching and bunching conditions. In this set, we prove that the non-uniformly hyperbolic maps are Cr open and there exists a Cr open and dense subset of continuity points for the center Lyapunov exponents. We also generalize these results to volume-preserving systems.