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Attractors for the non-autonomous dynamical systems. (English) Zbl 0971.37038
Fiedler, B. (ed.) et al., International conference on differential equations. Proceedings of the conference, Equadiff ’99, Berlin, Germany, August 1-7, 1999. Vol. 1. Singapore: World Scientific. 684-689 (2000).
The author introduces a concept of so-called pull back attractors for a general class of nonautonomous dynamical systems and gives sufficient conditions for the existence of such attractors. To do so the nonautonomous dynamical system is interpreted as a cocycle over the corresponding autonomous dynamical system. The pull back attractor for such cocycle is constructed in the spirit of the attractor theory for random dynamical systems [see H. Crauel and F. Flandoli, Attractors for random dynamical systems, Probab. Theory Relat. Fields 100, No. 3, 365-393 (1994; Zbl 0819.58023)]. The application of this construction to the nonautonomous 2D Navier-Stokes system is also given. Note that in contrast to the previous constructions of attractors for this system neither the compactness of the hull of the nonautonomous external force nor the boundedness of the external force as \(t\to\infty\) is required.
For the entire collection see [Zbl 0949.00019].

MSC:
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
35B41 Attractors
37B55 Topological dynamics of nonautonomous systems
37B25 Stability of topological dynamical systems
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