We present a formulation of the SRB (Sinai-Ruelle-Bowen) property for invariant measures of C 2 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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Qian et al. (2001) studied this question.
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