Abstract
A problem on the continuous nomarlization of nonautonomous parametrically-perturbed systems of differential equations with a constant linear part is examined. A class of nonautonomous systems is delineated, which leads to a continuous normal form of resonance type under a formal transformation with continuous coefficients bounded with respect to a parameter and to time. The structure of the normal form of almostperiodic systems is detailed. The results obtained are applied to the study of the problem on the birth of stationary modes in a neighborhood of the resonance.
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