Sensitivity and historic behavior for continuous maps on Baire metric spaces

Abstract We introduce a notion of sensitivity with respect to continuous real-valued bounded map which provides sufficient condition for transformation, acting on Baire metric space, exhibit generic subset points historic behavior (also known as irregular points). The applications this criterion recover, and extend, several theorems the genericity set, in addition yielding number new results, including information set geodesic flows, both negative non-positive curvature, semigroup actions.