Abstract. We prove that each closed and connected set $C \subseteq{\msbm R}^n$ is congruent to the $\omega $-limit set of a solution $x\colon[0,\infty ) \to{\msbm R}^{n+2}$ of $x'=f(x)$ for some bounded $f\in C^\infty({\msbm R}^{n+2},{\msbm R}^{n+2})$.

AMS Subject Classification (1991): 34C35, 34D45

Received June 8, 2000, and in revised form December 8, 2000. (Registered under 2780/2009.)