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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

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

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  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
  6. Some dynamical properties for free semigroup actions 2017, https://doi.org/10.1142/S0219493718500326
  7. Parameterized IFS with the Asymptotic Average Shadowing Property vol.15, pp.2, 2016, https://doi.org/10.1007/s12346-015-0184-6
  8. Asymptotic average shadowing property on compact metric spaces vol.69, pp.9, 2008, https://doi.org/10.1016/j.na.2007.08.058
  9. A Type of the Shadowing Properties for Generic View Points vol.7, pp.1, 2018, https://doi.org/10.3390/axioms7010018
  10. The ergodic shadowing property and homoclinic classes vol.2014, pp.1, 2014, https://doi.org/10.1186/1029-242X-2014-90