Abstract
This chapter discusses the classification of certain continuous flows. It explores dynamical systems where one of the positive prolongation, negative prolongation, or bilateral prolongation coincides with one of the positive limit set, negative limit set, or bilateral limit set at every point of the phase space. Of the nine types of flows formed in this manner, three of them are essential in the sense that any of the other nine is equivalent to one of these three types. In addition, if the phase space is compact, then all nine types of flows are equivalent. For planar flows of any of the nine types, either all points are critical or there is a single critical point that is a global Poincare center.
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