On R. A. Smith's autonomous convergence theorem
The authors study the autonomous system \(x'= f(x)\) on a domain \(D\) in \(\mathbb{R}^n\). They are concerned with the \(\alpha\)- and \(\omega\)-limit sets and develop sufficient conditions that these consist only of equilibria. In addition, they give sufficient conditions that any invariant set have Hausdorff dimension \(\leq 1\).
scientific article; zbMATH DE number 796927
scientific article