Continuous normal form of a class of nonautonomous parametrically- perturbed systems and its application (Q790323)

The author studies the continuous normalization of the parametrically perturbed system \(\dot z=A(\mu)z+\sum^{\infty}_{j=2}F^{(j)}(t,\mu,z)\), where \(F^{(j)}\) is a j-th order form with respect to \(z\in R^ n\) or \((C^ n)\). 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 almost-periodic 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.