Measure-theoretical properties of center foliations

Marcelo Viana; Jiagang Yang

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arXiv · 1603.03609

Measure-theoretical properties of center foliations

Marcelo Viana·Jiagang Yang

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Abstract

Center foliations of partially hyperbolic diffeomorphisms may exhibit pathological behavior from a measure-theoretical viewpoint: quite often, the disintegration of the ambient volume measure along the center leaves consists of atomic measures. We add to this theory by constructing stable examples for which the disintegration is singular without being atomic. In the context of diffeomorphisms with mostly contracting center direction, for which upper leafwise absolute continuity is known to hold, we provide examples where the center foliation is not lower leafwise absolutely continuous.

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Marcelo Viana, Jiagang Yang. 2016-03-11. Measure-theoretical properties of center foliations. https://arxiv.org/abs/1603.03609

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