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| A global attractor related to autonomous ordinary or partial differential equation is an invariant compact set attracting bounded sets forwards in time. However, when the system under consideration is non-autonomous, during the last twenty years two more or less disconnected approaches have been developed in order to study attractors for the associated non-autonomous dynamical systems. On the one hand, the pullback attractor, an invariant set for the evolution process which is pullback (but, in general, not forwards) attracting. On the other hand, the uniform attractor, a non-invariant compact set attracting uniformly forwards in time. The characterization of pullback attractors in terms of their internal structures and connecting dynamics has received an intensive research in the last years. This study, join to a careful description of the relationship between pullback and uniform attractors, leads to a detailed description of the uniform attractor, and to some results on the upper and lower semicontinuity, topological and structural stability of the uniform attractors associated to non-autonomous perturbations of a semigroup. |
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