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arXiv · 2308.05824

Topology of global attractors for homeomorphisms with the topological shadowing property in $\mathbb{R}^m$

Gonzalo Cousillas·Jorge Groisman
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Abstract

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.

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Gonzalo Cousillas, Jorge Groisman. 2023-08-10. Topology of global attractors for homeomorphisms with the topological shadowing property in $\mathbb{R}^m$. https://arxiv.org/abs/2308.05824

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