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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 n . They are concerned with the α- and ω-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 1.
MSC:
34D05Asymptotic stability of ODE
34D45Attractors
34C05Location of integral curves, singular points, limit cycles (ODE)
34C30Manifolds of solutions of ODE (MSC2000)