SKolmogorov-Bernoulli properties and the role of measure disintegration

Régis Varão (Unicamp)

We study the equivalence of the Kolmogorov Bernoulli properties for a certain class of partially hyperbolic diffeomorphism homotopic to a linear Anosov on the 3-torus. A crucial point in the proof is to understand atomic disintegration of volume on center leaves. More precisely our theorem states that the Kolmogorov and Bernoulli properties are equivalente for a volume preserving partially hyperbolic diffeomorphism on the 3-torus with absolutely continous center-stable foliation. This is a joint with G. Ponce (Unicamp) and A. Tahzibi (ICMC-USP)..