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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Hauptverfasser: Lin, Bohuan, Yao, Weijia, Cao, Ming
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Mathematics - Dynamical Systems
Mathematics - Optimization and Control
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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.
doi_str_mv 10.48550/arxiv.2202.00754
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title On Wilson's theorem about domains of attraction and tubular neighborhoods
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