# AVERAGE SHADOWING PROPERTIES ON COMPACT METRIC SPACES

• Park Jong-Jin (Department of Mathematics Chonbuk National University) ;
• Zhang Yong (Department of Mathematics Suzhou University)
• Published : 2006.04.01
• 131 30

#### 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

#### References

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6. Y. Zhang, On the average-shadowing property, Acta Scientiarum Naturalium Universitaties Pekinensis 37 (2001), 648-651

#### Cited by

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2. Symplectic diffeomorphisms with limit shadowing vol.10, pp.02, 2017, https://doi.org/10.1142/S1793557117500681
3. h–Average-Shadowing Property and Chaos vol.11, pp.1-2, 2013, https://doi.org/10.1080/1726037X.2013.823806
4. On partial shadowing of complete pseudo-orbits vol.411, pp.1, 2014, https://doi.org/10.1016/j.jmaa.2013.08.062
5. On partial shadowing of complete pseudo-orbits vol.404, pp.1, 2013, https://doi.org/10.1016/j.jmaa.2013.02.068