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Zbl 0841.34052
Li, Michael Y.; Muldowney, James S.
On R. A. Smith's autonomous convergence theorem.
(English)
[J] Rocky Mt. J. Math. 25, No.1, 365-379 (1995). ISSN 0035-7596

The authors study the autonomous system $x'= f(x)$ on a domain $D$ in $\bbfR^n$. 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 $\le 1$.
[A.Hausrath (Boise)]
MSC 2000:
*34D05 Asymptotic stability of ODE
34D45 Attractors
34C05 Qualitative theory of some special solutions of ODE
34C30 Manifolds of solutions of ODE

Keywords: Bendixson's criterion; Dulac criterion; center manifold; wandering points; autonomous system; $\alpha$- and $\omega$-limit sets; invariant set; Hausdorff dimension

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