On Wilson's theorem about domains of attraction and tubular neighborhoods

On Wilson's theorem about domains of attraction and tubular neighborhoods

In this paper, we show that the domain of attraction of a compact asymptotically stable submanifold of a finite-dimensional smooth manifold of an autonomous system is homeomorphic to its tubular neighborhood. The compactness of the attractor is crucial, without which this result is false; two counte...

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Veröffentlicht in:arXiv.org 2022-02
Hauptverfasser: Lin, Bohuan, Yao, Weijia, Cao, Ming
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Attraction
Domains
Manifolds (mathematics)
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description In this paper, we show that the domain of attraction of a compact asymptotically stable submanifold of a finite-dimensional smooth manifold of an autonomous system is homeomorphic to its tubular neighborhood. The compactness of the attractor is crucial, without which this result is false; two counterexamples are provided to demonstrate this.
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Manifolds (mathematics)
title On Wilson's theorem about domains of attraction and tubular neighborhoods
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