Abstract
The uniform asymptotical behavior of nonautonomous dynamical systems and their attractors is investigated. In particular, it is shown that parametrically inflated pullback attractors are uniformly forward attracting and, also that, under appropriate conditions, the component sets of the pullback attractor A of a system form an almost periodic setvalued mapping t → A θ t ( p ) when its driving system is almost periodic. This, together with the attraction properties of A , demonstrates that almost periodic systems exhibit global almost periodic asymptotic behavior.
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