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Recurrence, rigidity, and shadowing in dynamical systems

Volume 260 / 2023

Jonathan Meddaugh Fundamenta Mathematicae 260 (2023), 263-279 MSC: Primary 37B20; Secondary 37B65, 37B45. DOI: 10.4064/fm184-10-2022 Published online: 24 November 2022

Abstract

We examine the interplay between recurrence properties and the shadowing property in dynamical systems on compact metric spaces. In particular, we show that a uniformly rigid system $(X,f)$ has shadowing if and only if $X$ is totally disconnected, and use this to demonstrate the existence of a space $X$ for which no surjective system $(X,f)$ has shadowing. We further refine these results to discuss the dynamics that can occur in spaces with compact space of self-maps.

Authors

  • Jonathan MeddaughBaylor University
    Waco, TX 76798, USA
    e-mail

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