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A Note on Topological Average Shadowing Property Via Uniformity

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Abstract

We study topological ergodic shadowing, topological \(\underline{d}\) shadowing and topological average shadowing property for a continuous map on a uniform space and show that they are equivalent for a uniformly continuous map with topological shadowing on a compact uniform space. Furthermore, we prove that topological average shadowing property with Lyapunov stability implies topological ergodicity.

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Acknowledgements

The authors are grateful to anonymous reviewers for careful reading and valuable suggestions.

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Authors and Affiliations

  1. Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

    Seyyed Alireza Ahmadi

  2. School of Sciences, Southwest Petroleum University, Chengdu, 610500, Sichuan, People’s Republic of China

    Xinxing Wu

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  1. Seyyed Alireza Ahmadi
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  2. Xinxing Wu
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Correspondence to Seyyed Alireza Ahmadi.

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Ahmadi, S.A., Wu, X. A Note on Topological Average Shadowing Property Via Uniformity. Qual. Theory Dyn. Syst. 22, 84 (2023). https://doi.org/10.1007/s12346-023-00791-2

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