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 $C^r$ 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. 
Chao Liang, Karina Marin, Jiagang Yang
math.DS