• Park Jong-Jin (Department of Mathematics Chonbuk National University) ;
  • Zhang Yong (Department of Mathematics Suzhou University)
  • Published : 2006.04.01


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.


average shadowing property;${\delta}$-average-pseudo-orbit;shadowing property(pseudo orbit tracing property);${\delta}$-pseudo-orbit;chain recurrent


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