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Shadowing, sensitivity, and entropy points

Part of: Dynamical systems with hyperbolic behavior Topological dynamics

Published online by Cambridge University Press:  18 September 2025

Noriaki Kawaguchi
Noriaki Kawaguchi*
Affiliation:
Department of Mathematical and Computing Science, School of Computing, Institute of Science Tokyo , 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8552, Japan
*
e-mail: gknoriaki@gmail.com
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Abstract

For continuous self-maps of compact metric spaces, we explore the relationship among the shadowable points, sensitive points, and entropy points. Specifically, we show that (1) if the set of shadowable points is dense in the phase space, then any interior point of the set of sensitive points is an entropy point; and (2) if the topological entropy is zero, then the denseness of the set of shadowable points is equivalent to almost chain continuity. In addition, we present a counter-example to a question raised by Ye and Zhang regarding entropy points.

Keywords

Shadowingsensitivityentropychain continuitychain component

MSC classification

Primary: 37B40: Topological entropy 37D45: Strange attractors, chaotic dynamics

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Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 17
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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