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SRB measures and Pesin’s entropy formula for endomorphisms. (English) Zbl 1113.37010
Summary: 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.

MSC:
37C40 Smooth ergodic theory, invariant measures for smooth dynamical systems
37A35 Entropy and other invariants, isomorphism, classification in ergodic theory
37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
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