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arXiv · 2503.09745

Shadowing property on hyperspace of continua induced by Morse gradient system

Jelena Katić·Darko Milinković
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Abstract

It is known that Morse-Smale diffeomorphisms have the shadowing property; however, the question of whether $C(f)$ also has the shadowing property when $f$ is Morse-Smale remains open and has been resolved only in a few specific cases~\cite{AB}. We prove that if $f:M\to M$ is a time-one-map of Morse gradient flow, the induced map $C(f):C(M)\to C(M)$ on the hyperspace of subcontinua does not have the shadowing property.

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Jelena Katić, Darko Milinković. 2025-03-12. Shadowing property on hyperspace of continua induced by Morse gradient system. https://doi.org/10.1016/j.topol.2025.109693

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