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Non-absolutely continuous foliations. (English) Zbl 1137.37014
In this paper a partially hyperbolic diffeomorphism of a compact manifold preserving a smooth measure is studied. The authors prove that the foliation obtained fails to have the absolute continuous property. They do this by showing that the sum of Lyapunov exponents in the central direction is not zero on a set of positive measure. The authors extend the results to general foliations with compact leaves.

MSC:
37D30 Partially hyperbolic systems and dominated splittings
37C85 Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\)
57R30 Foliations in differential topology; geometric theory
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