Regular points for ergodic sinai measures

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Ergodic properties of smooth dynamical systems are considered. A point is called regular for an ergodic measure μ if it is generic for μ and the Lyapunov exponents at it coincide with those of μ. We show that an ergodic measure with no zero Lyapunov exponent is absolutely continuous with respect to unstable foliation [L] if and only if the set of all points which are regular for it has positive Lebesgue measure.

Original languageEnglish
Pages (from-to)747-766
Number of pages20
JournalTransactions of the American Mathematical Society
Volume328
Issue number2
DOIs
Publication statusPublished - Dec 1991
Externally publishedYes

Fingerprint

Ergodic Measure
Lyapunov Exponent
Dynamical systems
Lebesgue Measure
Absolutely Continuous
Foliation
Dynamical system
Unstable
If and only if
Zero

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

Regular points for ergodic sinai measures. / Tsujii, Masato.

In: Transactions of the American Mathematical Society, Vol. 328, No. 2, 12.1991, p. 747-766.

Research output: Contribution to journalArticle

@article{8a632762e5484a47bab70023c726d761,
title = "Regular points for ergodic sinai measures",
abstract = "Ergodic properties of smooth dynamical systems are considered. A point is called regular for an ergodic measure μ if it is generic for μ and the Lyapunov exponents at it coincide with those of μ. We show that an ergodic measure with no zero Lyapunov exponent is absolutely continuous with respect to unstable foliation [L] if and only if the set of all points which are regular for it has positive Lebesgue measure.",
author = "Masato Tsujii",
year = "1991",
month = "12",
doi = "10.1090/S0002-9947-1991-1072103-1",
language = "English",
volume = "328",
pages = "747--766",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "2",

}

TY - JOUR

T1 - Regular points for ergodic sinai measures

AU - Tsujii, Masato

PY - 1991/12

Y1 - 1991/12

N2 - Ergodic properties of smooth dynamical systems are considered. A point is called regular for an ergodic measure μ if it is generic for μ and the Lyapunov exponents at it coincide with those of μ. We show that an ergodic measure with no zero Lyapunov exponent is absolutely continuous with respect to unstable foliation [L] if and only if the set of all points which are regular for it has positive Lebesgue measure.

AB - Ergodic properties of smooth dynamical systems are considered. A point is called regular for an ergodic measure μ if it is generic for μ and the Lyapunov exponents at it coincide with those of μ. We show that an ergodic measure with no zero Lyapunov exponent is absolutely continuous with respect to unstable foliation [L] if and only if the set of all points which are regular for it has positive Lebesgue measure.

UR - http://www.scopus.com/inward/record.url?scp=0141842192&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0141842192&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-1991-1072103-1

DO - 10.1090/S0002-9947-1991-1072103-1

M3 - Article

AN - SCOPUS:0141842192

VL - 328

SP - 747

EP - 766

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 2

ER -