For a continuous flow on a topological space the concept of a nonwandering point (in forward/backward time) is well-known. Another useful concept (for example from the point of view of scattering theory) is that of a trapped point, by which I mean a point whose orbit has compact closure. Under some conditions (such as uniform hyperbolicity) on the flow and the space, the trapped points seem to coincide with those that are nonwandering both in forward and backward time. However, I don't have a good overview here and I would appreciate some references and remarks on the discussion of equivalence between trapped and nonwandering points.
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