Abstract
The authors introduce the concepts of the eventual shadowing property and eventually shadowable point for set-valued dynamical systems and prove that a set-valued dynamical system has the eventual shadowing property if and only if every point in the phase space is eventually shadowable; every chain transitive set-valued dynamical system has either the eventual shadowing property or no eventually shadowable points; and a set-valued dynamical system admits an eventually shadowable point if and only if it admits a minimal eventually shadowable point. Moreover, it is proved that a set-valued dynamical system with the eventual shadowing property is chain mixing if and only if it is mixing and if and only if it has the specification property.
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The authors wish to thank the referees for the valuable suggestions.
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Supported by the National Natural Science Foundation of China (Grant Nos. 12061043, 11661054, 11261039)
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Xie, X.R., Yin, J.D. On the Eventual Shadowing Property and Eventually Shadowable Point of Set-valued Dynamical Systems. Acta. Math. Sin.-English Ser. 38, 1105–1115 (2022). https://doi.org/10.1007/s10114-022-1041-6
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DOI: https://doi.org/10.1007/s10114-022-1041-6