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On R. A. Smith’s autonomous convergence theorem. (English) Zbl 0841.34052
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 \(\leq 1\).
Reviewer: A.Hausrath (Boise)

MSC:
34D05 Asymptotic properties of solutions to ordinary differential equations
34D45 Attractors of solutions to ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C30 Manifolds of solutions of ODE (MSC2000)
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