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http://dx.doi.org/10.4134/CKMS.2006.21.2.355

AVERAGE SHADOWING PROPERTIES ON COMPACT METRIC SPACES  

Park Jong-Jin (Department of Mathematics Chonbuk National University)
Zhang Yong (Department of Mathematics Suzhou University)
Publication Information
Communications of the Korean Mathematical Society / v.21, no.2, 2006 , pp. 355-361 More about this Journal
Abstract
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;
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