Abstract
In this paper, we show that the domain of attraction of a compact asymptotically stable submanifold in a finite-dimensional smooth manifold of an autonomous system is homeomorphic to the submanifold’s tubular neighborhood. The compactness of the submanifold is crucial, without which this result is false; two counterexamples are provided to demonstrate this. • We show a fundamental result about the domain of attraction of a compact asymptotically stable submanifold. • We provide counterexamples to emphasize the key role of the compactness of the submanifold. • The aforementioned result refines the existing one and facilitates the topological analysis of autonomous systems.
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