On genericity of shadowing in one dimension

Abstract

We show that shadowing is a generic property among continuous maps and surjections on a large class of locally connected one-dimensional dynamical systems.

S-limit shadowing is generic for continuous Lebesgue measure preserving circle maps

“…Mizera proved [19] that shadowing is a generic property in the class of continuous maps of the interval or circle. Recently, these results were extended to many other one-dimensional spaces, see [11,14,20]. It turned out that non-invertibility is not an obstacle to obtain genericity of shadowing also in higher dimension [15].…”

“…By Lemma 18 the partition Q m(i) and δ = δ m(i) > 0 were chosen for α-shadowing with α = 1/m(i). Fix k so that (20) 4/k < δ.…”