Topology of global attractors for homeomorphisms with the topological shadowing property in $\mathbb{R}^m$
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914423185080320 |
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| author | Cousillas, Gonzalo Groisman, Jorge |
| author_facet | Cousillas, Gonzalo Groisman, Jorge |
| contents | This paper studies the behavior of dynamical systems in non-compact spaces, specifically focusing on the concepts of global attractors and shadowing. Let $K$ be a compact global attractor. We show that the shadowing property holds in certain types of dynamical systems in non-compact spaces if and only if $K$ is trivial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_05824 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Topology of global attractors for homeomorphisms with the topological shadowing property in $\mathbb{R}^m$ Cousillas, Gonzalo Groisman, Jorge Dynamical Systems This paper studies the behavior of dynamical systems in non-compact spaces, specifically focusing on the concepts of global attractors and shadowing. Let $K$ be a compact global attractor. We show that the shadowing property holds in certain types of dynamical systems in non-compact spaces if and only if $K$ is trivial. |
| title | Topology of global attractors for homeomorphisms with the topological shadowing property in $\mathbb{R}^m$ |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2308.05824 |