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In this work we study relations between regularity of invariant foliationsand Lyapunov exponents of partially hyperbolic diffeomorphisms. We suggest anew regularity condition for foliations in terms of desintegration of Lebesguemeasure which can be considered as a criterium for rigidity of Lyapunovexponents.

Regularity of foliations and Lyapunov exponents of partially hyperbolic dynamics