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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Regular points for ergodic Sinaĭ measures


Author: Masato Tsujii
Journal: Trans. Amer. Math. Soc. 328 (1991), 747-766
MSC: Primary 58F11
DOI: https://doi.org/10.1090/S0002-9947-1991-1072103-1
MathSciNet review: 1072103
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Abstract: Ergodic properties of smooth dynamical systems are considered. A point is called regular for an ergodic measure $ \mu $ if it is generic for $ \mu $ and the Lyapunov exponents at it coincide with those of $ \mu $. 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.


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DOI: https://doi.org/10.1090/S0002-9947-1991-1072103-1
Article copyright: © Copyright 1991 American Mathematical Society