We study continuous maps of an interval into itself. We find the necessary and sufficient condition for the maps of the type 2" to have the shadowing property. Further we show that any chaotic map, which has only cycles of order a power of 2, does not have the shadowing property. Introduction Let /:/(=(0;l))—»7 be a continuous map of the interval 7 to itself (i.e., / G C°(7, 7)). The orbit of x...

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.