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SRB measures and Pesin's entropy formula for endomorphisms


Authors: Min Qian and Shu Zhu
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
Published electronically: November 21, 2001
MathSciNet review: 1873014
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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.


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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

DOI: https://doi.org/10.1090/S0002-9947-01-02792-1
Keywords: Entropy, Lyapunov exponent, SRB measure
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
Article copyright: © Copyright 2001 American Mathematical Society

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