Regularity of foliations and Lyapunov exponents of partially hyperbolic   dynamics
  In this work we study relations between regularity of invariant foliations and Lyapunov exponents of partially hyperbolic diffeomorphisms. We suggest a new regularity condition for foliations in terms of desintegration of Lebesgue measure which can be considered as a criterium for rigidity of Lyapunov exponents. 
Fernando Micena and Ali Tahzibi
math.DS