Abstract
In this paper, we generalize the notion of the ergodic shadowing property to the iterated function systems and prove some related theorems on this notion. In addition, we give an example to show that there is an iterated function system which has the ergodic shadowing property but not weakly mixing. Moreover, we show that ergodic shadowing property implies the average shadowing property for iterated function systems.
Similar content being viewed by others
References
Aoki, N.: Chapter 15 topological dynamics. N.-Holl. Math. Libr. 41, 625–740 (1989)
Bahabadi, A.Z.: Shadowing and average shadowing properties for iterated function systems. Georgian Math. J. 22, 179–184 (2015)
Blank, M.L.: Metric properties of \(\varepsilon \)-trajectories of dynamical systems with stochastic behaviour. Ergod. Theory Dyn. Syst. 8, 365–378 (1988)
Blank, M.L.: Deterministic properties of stochastically perturbed dynamic systems. Theory Probab. Appl. 33, 612–623 (1989)
Dastjerdi, D.A., Hosseini, M.: Sub-shadowings. Nonlinear Anal. 72, 3759–3766 (2010)
Fatehi, N.M.: Parameterized IFS with the asymptotic average shadowing property. Qual. Theory Dyn. Syst. 15, 367–381 (2016)
Fakhari, A., Ghane, F.H.: On shadowing: ordinary and ergodic. J. Math. Anal. Appl. 364, 151–155 (2010)
Glavan, V., Gutu, V.: Shadowing in parameterized IFS. Fixed Point Theory 7, 263–274 (2006)
Hui, H., Ma, D.: Some dynamical properties for free semigroup actions. Stoch. Dyn. 18, 179–184 (2018)
Nia, M.F.: Iterated function system with the average shadowing property. Topol. Proc. 48, 261–275 (2016)
Shabani, Z.: Ergodic shadowing of semigroup action. Bull. Iran. Math. Soc. 46, 303–321 (2020)
Wang, H., Fu, H., Diao, S., Zeng, P.: Chain mixing, shadowing properties and multi-transitivity. Bull. Iran. Math. Soc. 45, 1605–1618 (2019)
Wu, X., Wang, L., Liang, J.: The Chain properties and average shadowing property of iterated function systems. Qual. Theory Dyn. Syst. 17, 219–227 (2018)
Acknowledgements
The authors are grateful to the referees for the careful reading and many valuable comments.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Rosihan M. Ali.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supported by National Nature Science Funds of China (11771149)
Rights and permissions
About this article
Cite this article
Wang, H., Liu, Q. Ergodic Shadowing Properties of Iterated Function Systems. Bull. Malays. Math. Sci. Soc. 44, 767–783 (2021). https://doi.org/10.1007/s40840-020-00976-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40840-020-00976-x