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Asymptotic method for the investigation of m-frequency oscillation systems

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Abstract

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.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    A. M. Samoilenko

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  1. A. M. Samoilenko
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 10, pp. 1366–1387, October, 1998.

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Samoilenko, A.M. Asymptotic method for the investigation of m-frequency oscillation systems. Ukr Math J 50, 1559–1585 (1998). https://doi.org/10.1007/BF02513504

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  • DOI: https://doi.org/10.1007/BF02513504

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