  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 $C^r$ open and there exists a $C^r$ open and dense subset of
continuity points for the center Lyapunov exponents. We also generalize these
results to volume-preserving systems.
