Regular points for ergodic sinai measures

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7 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

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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