On the reduction to a subspace of stability properties of systems in metric spaces
The authors deal with dynamical and semi-dynamical systems on metric spaces. Assume that two invariant subsets \(M\), \(Y\) are given, with \(M\) compact and \(M\subset Y\). The reduction problem consists in the following. If \(M\) is stable (or asymptotically stable) for the restriction of the dynamical system to \(Y\), under what additional assumptions is it possible to deduce that \(M\) is stable (or asymptotically stable) for the whole system? The authors prove several theorems about this problem, and compare their results to early achievements in the existing literature. In particular, the role of uniformity in the behaviour of the dynamical system is emphasized. As examples, systems in triangular form and systems with delays are discussed.
scientific article; zbMATH DE number 878434