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Topological Average Shadowing Property on Uniform Spaces

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Abstract

We introduce topological definition of average shadowing property. We prove that topological average shadowing property implies topological chain transitivity. In particular it is proved that for a dynamical system with dense minimal points, the topological average shadowing property implies topological strong ergodicity.

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Acknowledgements

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

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Authors and Affiliations

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

    Farzaneh Pirfalak, Seyyed Alireza Ahmadi & Nader Kouhestani

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

    Xinxing Wu

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  1. Farzaneh Pirfalak
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  2. Seyyed Alireza Ahmadi
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  3. Xinxing Wu
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  4. Nader Kouhestani
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Correspondence to Seyyed Alireza Ahmadi.

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Pirfalak, F., Ahmadi, S.A., Wu, X. et al. Topological Average Shadowing Property on Uniform Spaces. Qual. Theory Dyn. Syst. 20, 31 (2021). https://doi.org/10.1007/s12346-021-00466-w

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