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

2022/02/01 by Lin, Bohuan, Yao, Weijia, Cao, Ming · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2202.00754

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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