Asymptotic pseudotrajectories and chain recurrent flows, with applications

We present a general framework to study compact limit sets of trajectories for a class of nonautonomous systems, including asymptotically autonomous differential equations, certain stochastic differential equations, stochastic approximation processes with decreasing gain, and fictitious plays in game theory. Such limit sets are shown to be internally chain recurrent, and conversely. © 1996 Plenum Publishing Corporation