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arXiv · 2202.00754

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

Bohuan Lin·Weijia Yao·Ming Cao
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Abstract

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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Bohuan Lin, Weijia Yao, Ming Cao. 2022-02-01. On Wilson's theorem about domains of attraction and tubular neighborhoods. https://arxiv.org/abs/2202.00754

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