Genericity of historic behavior for maps and flows

Abstract We establish a sufficient condition for continuous map, acting on compact metric space, to have Baire residual set of points exhibiting historic behavior (also known as irregular points). This criterion applies, instance, minimal and non-uniquely ergodic map; maps preserving two distinct probability measures with full support; non-trivial homoclinic classes; some non-uniformly expanding maps; partially hyperbolic diffeomorphisms periodic whose stable manifolds are dense, including Mañé Shub examples robustly transitive non-hyperbolic diffeomorphisms. way, our unifying approach recovers collection deep theorems the genericity set, both additive sub-additive potentials, also provides number new applications.