Topology of global attractors for homeomorphisms with the topological shadowing property in ℝ^m

2023/08/10 by Gonzalo Cousillas, Cousillas, Gonzalo, Groisman, Jorge
Engineering · Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2308.05824

openalex publication_date 2023/08/10 · openalex created_date 2023/08/15 · openalex updated_date 2026/07/28

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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