In this article we describe selected topological and dynamical properties of asymptotically periodic motions in continuous dynamical systems (flows). The main result is to show Lagrange stability (i.e. the closure of positive orbit is compact) of such motion with the aid of topological properties of limit sets. Two sufficient conditions for this kind of stability are provided: the value of asymptotic...
We introduce the notions of asymptotic period and asymptotically periodic orbits in metric spaces. We study some properties of these notions and their connections with ω-limit sets. We also discuss the notion of growth rate of such orbits and describe its properties in an extreme case.
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