G.Ochs, Random attractors: robustness, numerics and chaotic dynamics, in Ergodic Theory, Analysis, and E#cient Simulation of Dynamical Systems, Editor: B. Fiedler, Springer--Verlag, Heidelberg, 2001.  Home/Search   Document Not in Database   Summary   Related Articles

.... u t taking values in a nonempty compact set U t , thus (2) generates a nonautonomous di#erence inclusion of the form (1) with F t (x) f t (x, U t ) Other sources of examples are the discretization or time 1 mappings of di#erential control systems or di#erential equations without uniqueness [3, 7, 8, 9]. The mappings F t , which are usually assumed to be compact valued and upper semi continuous, may vary in some regular or completely arbitrarily fashion. The discrete time system generated by (1) is thus nonautonomous and no longer enjoys a setvalued semigroup property, so many of the concepts ....

....is a generalisation of the positive invariance property of a semigroup. Note that the pullback convergence property (6) does not describe the convergence of #(t, t 0 ,D)ast ##. See [4, 5, 6] for a discussion on these properties in the context of singlevalued processes. The following theorem from [7, 9] is a generalisation of Theorem 3.1 to the nonautonomous case. 5 Theorem 3.4 Let # be a setvalued di#erence process with a positive invariant pullback absorbing family B = B t ,t# Z . Then there exists a pullback attractor A = A t ,t# Z which is uniquely determined by #(t 0 ,t 0 n, B t ....

G.Ochs, Random attractors: robustness, numerics and chaotic dynamics, in Ergodic Theory, Analysis, and E#cient Simulation of Dynamical Systems, Editor: B. Fiedler, Springer--Verlag, Heidelberg, 2001.

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