Asymptotic method for the investigation of m-frequency oscillation systems

We describe an asymptotic method for the integration of m-frequency oscillation systems of order 2n, analyze averaged equations in nonresonance and resonance cases, prove a theorem on the preservation of smooth p-dimensionai invariant tori under perturbation for any 0 ≤ p ≤ n, and indicate forms of decomposable m-frequency oscillation systems. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 10, pp. 1366–1387, October, 1998.