Abstract
In this article, the authors introduce the concept of shadowable points for set-valued dynamical systems, the pointwise version of the shadowing property, and prove that a set-valued dynamical system has the shadowing property iff every point in the phase space is shadowable; every chain transitive set-valued dynamical system has either the shadowing property or no shadowable points; and for a set-valued dynamical system there exists a shadowable point iff there exists a minimal shadowable point. In the end, it is proved that a set-valued dynamical system with the shadowing property is totally transitive iff it is mixing and iff it has the specification property.
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Supported by the National Natural Science Foundation of China (Grant Nos. 11661054, 11261039)
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Luo, X.F., Nie, X.X. & Yin, J.D. On the Shadowing Property and Shadowable Point of Set-valued Dynamical Systems. Acta. Math. Sin.-English Ser. 36, 1384–1394 (2020). https://doi.org/10.1007/s10114-020-9331-3
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DOI: https://doi.org/10.1007/s10114-020-9331-3