Communications of the
Korean Mathematical Society CKMS

We prove that if a continuous surjective map $f$ on a compact metric space $X$ has the average shadowing property, then every point $x$ is chain recurrent. We also show that if a homeomorphism $f$ has more than two fixed points on $S^1$, then $f$ does not satisfy the average shadowing property. Moreover, we construct a homeomorphism on a circle which satisfies the shadowing property but not the average shadowing property. This shows that the converse of the theorem 1.1 in [6] is not true.

Keywords: average shadowing property, $\delta$-average-pseudo-orbit, shadowing property(pseudo orbit tracing property), $\delta$-pseudo-orbit, chain recurrent

MSC numbers: 54H20, 58F99