On Shadowing System Generated by a Uniformly Convergent Mappings Sequence

Abstract

The shadowing property relationship between a uniformly convergent mapping sequence ${(f_{n})_{n=1}^{\infty }}$ and its limit mapping f in non-autonomous systems is discussed. Some sufficient and necessary conditions are given for that ${(f_{n})_{n=1}^{\infty }}$ is limit shadowing property, $\underline {d}$-shadowing property or pseudo-orbit shadowing property. In particular, a computer simulation of an example is given to illustrate the shadowing property of ${(f_{n})_{n=1}^{\infty }}$. In addition, it is proved that the sensitivity of ${(f_{n})_{n=1}^{\infty }}$ is equivalent to the sensitivity of f under the shadowing system.