Minimal yet measurable foliations
Gabriel Ponce Ali Tahzibi Régis Varão
Journal of Modern Dynamics 2014, 8(1): 93-107 doi: 10.3934/jmd.2014.8.93
In this paper we mainly address the problem of disintegration of Lebesgue measure along the central foliation of volume-preserving diffeomorphisms isotopic to hyperbolic automorphisms of 3-torus. We prove that atomic disintegration of the Lebesgue measure (ergodic case) along the central foliation has the peculiarity of being mono-atomic (one atom per leaf). This implies the measurability of the central foliation. As a corollary we provide open and nonempty subset of partially hyperbolic diffeomorphisms with minimal yet measurable central foliation.
keywords: disintegration minimal foliations Partial hyperbolicity measurable partitions Lyapunov exponents. derived from Anosov

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