Sinai–Ruelle–Bowen measures for weakly expanding maps

Abstract

We construct Sinai–Ruelle–Bowen measures for endomorphisms satisfying conditions far weaker than the usual non-uniform expansion. As a consequence, the definition of a non-uniformly expanding map can be weakened. We also prove the existence of an absolutely continuous invariant measure for local diffeomorphisms, only assuming the existence of hyperbolic times for Lebesgue at almost every point in the manifold.