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Non-absolutely continuous foliations

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Abstract

We consider a partially hyperbolic diffeomorphism of a compact smooth manifold preserving a smooth measure. Assuming that the central distribution is integrable to a foliation with compact smooth leaves we show that this foliation fails to have the absolute continuity property provided that the sum of Lyapunov exponents in the central direction is not zero on a set of positive measure. We also establish a more general version of this result for general foliations with compact leaves.

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Authors and Affiliations

  1. Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima, 739-8526, Japan

    Michihiro Hirayama

  2. Department of Mathematics, Pennsylvania State University, University Park, State College, PA, 16802, USA

    Yakov Pesin

Authors
  1. Michihiro Hirayama
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  2. Yakov Pesin
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Additional information

Partially supported by JSPS.

Partially supported by National Science Foundation grant #DMS-0088971 and U.S.-Mexico Collaborative Research grant 0104675.

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Hirayama, M., Pesin, Y. Non-absolutely continuous foliations. Isr. J. Math. 160, 173–187 (2007). https://doi.org/10.1007/s11856-007-0060-4

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  • DOI: https://doi.org/10.1007/s11856-007-0060-4

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