A new approach based on the analysis of influence a single perturbation is proposed as test for shadowing property broad class dynamical systems (in particular, non-autonomous) under variety perturbations. Applications several interesting cases are considered in detail.

Abstract In this paper we show that generic continuous Lebesgue measure-preserving circle maps have the s-limit shadowing property. addition, obtain is a property also for maps. particular, implies classical shadowing, periodic and limit are in these two settings as well.