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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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SRB measures and Pesin’s entropy formula for endomorphisms
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by Min Qian and Shu Zhu PDF
Trans. Amer. Math. Soc. 354 (2002), 1453-1471 Request permission

Abstract:

We present a formulation of the SRB (Sinai-Ruelle-Bowen) property for invariant measures of $C^2$ endomorphisms (maybe non-invertible and with singularities) of a compact manifold via their inverse limit spaces, and prove that this property is necessary and sufficient for Pesin’s entropy formula. This result is a non-invertible endomorphisms version of a result of Ledrappier, Strelcyn and Young.
References
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Additional Information
  • Min Qian
  • Affiliation: School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China
  • Shu Zhu
  • Affiliation: School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China
  • Received by editor(s): January 27, 1999
  • Received by editor(s) in revised form: December 21, 1999
  • Published electronically: November 21, 2001
  • Additional Notes: This research is supported by the National Natural Science Foundation of China
    The first author supported by the Special Funds for Major State Basic Research Projects
  • © Copyright 2001 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 354 (2002), 1453-1471
  • MSC (1991): Primary 58F11; Secondary 28D05, 28D20
  • DOI: https://doi.org/10.1090/S0002-9947-01-02792-1
  • MathSciNet review: 1873014