Shadowing property on hyperspace of continua induced by Morse gradient system
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912918483763200 |
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| author | Katić, Jelena Milinković, Darko |
| author_facet | Katić, Jelena Milinković, Darko |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_09745 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Shadowing property on hyperspace of continua induced by Morse gradient system Katić, Jelena Milinković, Darko Dynamical Systems 37B35 (Primary) 54F16, 37B40, 37B45, 37B25 (Secondary) 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. |
| title | Shadowing property on hyperspace of continua induced by Morse gradient system |
| topic | Dynamical Systems 37B35 (Primary) 54F16, 37B40, 37B45, 37B25 (Secondary) |
| url | https://arxiv.org/abs/2503.09745 |