The perturbation of attractors of skew-product flows with a shadowing driving system

The influence of the driving system on a skew-product flow generated by a t riangular system of differential equations can be perturbed in two ways, di rectly by perturbing the vector field of the driving system component itsel f or indirectly by perturbing its input variable in the vector field of the coupled component. The effect of such perturbations on a nonautonomous att ractor of the driven component is investigated here. In particular, it is s hown that a perturbed nonautonomous attractor with nearby components exists in the indirect case if the driven system has an inflated nonautonomous at tractor and that the direct case can be reduced to this case if the driving system is shadowing.