Geodesic
Shadowing and the basins of terminal chain components
Canadian mathematical bulletin, Tome 68 (2025) no. 1, pp. 187-197

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DOI

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.
DOI : 10.4153/S0008439524000730
Mots-clés : Shadowing, basin, chain component, generic, chain continuous 
Kawaguchi, Noriaki. Shadowing and the basins of terminal chain components. Canadian mathematical bulletin, Tome 68 (2025) no. 1, pp. 187-197. doi: 10.4153/S0008439524000730
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