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Relation between different types of global attractors of set-valued nonautonomous dynamical systems. (English) Zbl 1087.37016
The authors study the relation between forward and pullback attractors of set-valued nonautonomous dynamical systems. They prove that every compact global forward attractor is also a pullback attractor of the set-valued nonautonomous dynamical system. The inverse statement, generally speaking, is not true, but they prove that every global pullback attractor of an \(\alpha\)-condensing set-valued cocycle is always a local forward attractor. The obtained results are applied to periodic and homogeneous systems. The authors give also a new criterion for the absolute asymptotic stability of nonstationary discrete linear inclusions.

MSC:
37B55 Topological dynamics of nonautonomous systems
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
37B25 Stability of topological dynamical systems
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
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