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Shadowing and the basins of terminal chain components

Published online by Cambridge University Press:  10 December 2024

Noriaki Kawaguchi
Noriaki Kawaguchi*
Affiliation:
Research Institute of Science and Technology, Tokai University, 4-1-1 Kitakaname, Hiratsuka, Kanagawa 259-1292, Japan
*
e-mail: [email protected]
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Abstract

We provide an alternative view of some results in [1, 3, 11]. In particular, we prove that (1) if a continuous self-map of a compact metric space has the shadowing, then the union of the basins of terminal chain components is a dense $G_\delta $-subset of the space; and (2) if a continuous self-map of a locally connected compact metric space has the shadowing, and if the chain recurrent set is totally disconnected, then the map is almost chain continuous.

Keywords

Shadowingbasinchain componentgenericchain continuous
Type
Article
Information
Canadian Mathematical Bulletin , Volume 68 , Issue 1 , March 2025 , pp. 187 - 197
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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