# Article

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Keywords:
$\omega$-limit sets; stationary points; the Poincar'{e}-Bendixon theorem
Summary:
In this paper the $\omega$-limit behaviour of trajectories of solutions of ordinary differential equations is studied by methods of an axiomatic theory of solution spaces. We prove, under very general assumptions, semi-invariance of $\omega$-limit sets and a Poincar'{e}-Bendixon type theorem.
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