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The relationship between pullback, forward and global attractors

Various types of attractors are considered and compared for nonautonomous dynamical systems involving a cocycle state space mapping that is driven by an autonomous dynamical system on a compact metric space. In particular, conditions are given for a uniform pullback attractor of the cocycle mapping to form a global attractor of the associated autonomous skew–product semi–dynamical system. The results are illustrated with several examples that are generated by differential equations on a Banach space with a uniformly dissiptative structure induced by a montone operator.