A Simple Example of Pathological Foliations in Skew-Product Diffeomorphisms
Abstract
Inspired by examples of Katok and Milnor Milnor1997, we construct simple examples of skew-product volume preserving diffeomorphism where the center foliation is pathological in the sense that, there is a full measure set whose intersection with any center leaf contains at most one point. Comparing with other examples in literature, our mechanism for producing such pathological foliation is simple and elementary.
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