SRB measures and Pesin’s entropy formula for endomorphisms

Qian, Min; Zhu, Shu

doi:10.1090/S0002-9947-01-02792-1

SRB measures and Pesin’s entropy formula for endomorphisms
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by Min Qian and Shu Zhu

Trans. Amer. Math. Soc. 354 (2002), 1453-1471

DOI: https://doi.org/10.1090/S0002-9947-01-02792-1

Published electronically: November 21, 2001

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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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