Non-absolutely continuous foliations

Michihiro Hirayama, Yakov B. Pesin

Research output: Contribution to journalArticle

14 Citations (Scopus)

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

Fingerprint

Foliation
Leaves
Absolute Continuity
Smooth Manifold
Diffeomorphism
Compact Manifold
Lyapunov Exponent
Zero

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Hirayama, Michihiro ; Pesin, Yakov B. / Non-absolutely continuous foliations. In: Israel Journal of Mathematics. 2007 ; Vol. 160. pp. 173-187.
@article{7049d9721f3643bfab8d9c5bb40202c6,
title = "Non-absolutely continuous foliations",
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.",
author = "Michihiro Hirayama and Pesin, {Yakov B.}",
year = "2007",
month = "8",
day = "1",
doi = "10.1007/s11856-007-0060-4",
language = "English (US)",
volume = "160",
pages = "173--187",
journal = "Israel Journal of Mathematics",
issn = "0021-2172",
publisher = "Springer New York",

}

Non-absolutely continuous foliations. / Hirayama, Michihiro; Pesin, Yakov B.

In: Israel Journal of Mathematics, Vol. 160, 01.08.2007, p. 173-187.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Non-absolutely continuous foliations

AU - Hirayama, Michihiro

AU - Pesin, Yakov B.

PY - 2007/8/1

Y1 - 2007/8/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=53949083437&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=53949083437&partnerID=8YFLogxK

U2 - 10.1007/s11856-007-0060-4

DO - 10.1007/s11856-007-0060-4

M3 - Article

VL - 160

SP - 173

EP - 187

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

ER -