The approximate decomposition of exponential order of slow–fast motions in multifrequency systems

This paper deals with multifrequency slow–fast systems. It is shown that, under a suitable change of coordinates, the system can be reduced to a simple form such that slow motions are described by autonomous equations except for exponential error of perturbations. Hence, the fast and slow motions are decoupled. The Newton rapid iteration is used. In addition, for a perturbation, only the smallness condition is needed.