Non-absolutely continuous foliations

Michihiro Hirayama, Yakov Pesin

Research output: Contribution to journalArticle

14 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)173-187
Number of pages15
JournalIsrael Journal of Mathematics
Volume160
DOIs
StatePublished - Aug 1 2007

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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