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Strong Chain Transitivity via Uniformity

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Abstract

We introduce topological definitions of strong chain transitivity and we prove that topological average shadowing and topological pseudo-orbital specification each imply topological strong chain transitivity. Furthermore, we introduce the notion of the topological Lipschitz property and we show that it is a sufficient condition for the coincidence of the strong chain recurrent set of a dynamical system and its iterations.

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Acknowledgements

The author greatly appreciates the referees valuable comments and suggestions.

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

    Seyyed Alireza Ahmadi

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  1. Seyyed Alireza Ahmadi
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Ahmadi, S.A. Strong Chain Transitivity via Uniformity. Qual. Theory Dyn. Syst. 23, 123 (2024). https://doi.org/10.1007/s12346-024-00983-4

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