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Attractors for nonautonomous and random dynamical systems perturbed by impulses
Nonautonomous and random dynamical systems perturbed by impulses are considered.
The impulses form a flow. Over this flow the perturbed system also has
the structure of a new nonautonomous/random dynamical system. The long time behavior of
this system is considered. In particular the existence of an attractor is proven.
The result can be applied to a large class of dissipative systems given by
partial or ordinary differential equations. As an example of this class of problems the
Lorenz system is studied. For another problem given by a one-dimensional affine differential
equation and perturbed by affine impulses, the attractor can be calculated explicitly.