SRB measures for weakly expanding maps

Abstract

We construct SRB measures for endomorphisms satisfying conditions far weaker than the non-uniformly expansion. As a consequence, the definition of 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 almost all point of the manifold.

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• Adapted random perturbations for non-uniformly expanding maps
• Physical Measure and Absolute Continuity for One-Dimensional Center Direction
• Gibbs-Markov-Young structures with (stretched) exponential tail for partially hyperbolic attractors
• Lift and Synchronization
• Non-uniform hyperbolicity and existence of absolutely continuous invariant measures
• Physical measures for mostly sectional expanding flows