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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Regular points for ergodic Sinaĭ measures
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by Masato Tsujii PDF
Trans. Amer. Math. Soc. 328 (1991), 747-766 Request permission

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 $[\text {L}]$ if and only if the set of all points which are regular for it has positive Lebesgue measure.
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • 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