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Averaging with regard to resonance relations between frequencies in oscillatory systems

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Literature cited

  1. N. N. Bogolyubov and Yu. A. Mitropol'skii, Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  2. V. I. Arnol'd, “Conditions for the applicability and bounds for the error in the method of averaging for systems which pass through resonance in the evolution process,” Dokl. Akad. Nauk SSSR,161, No. 1, 9–12 (1965).

    Google Scholar 

  3. M. M. Khapaev, “On averaging and an analysis of stability in multifrequency systems of ordinary differential equations,” in: Problems in Mathematical Physics and Computational Mathematics [in Russian], Nauka, Moscow (1977), pp. 298–307.

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  4. E. A. Grebenikov and Yu. A. Ryabov, New Qualitative Methods in Celestial Mechanics [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  5. E. A. Grebenikov and Yu. A. Ryabov, Resonances and Small Denominators in Celestial Mechanics [in Russian], Nauka, Moscow (1978).

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  6. N. I. Popova, “On averaging with respect to fast variables in multifrequency systems with resonances,” ITEF Preprint No. 70, Moscow (1977), pp. 1–30.

  7. A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs (1964).

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 33, No. 2, pp. 262–267, March–April, 1981.

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Petrishin, R.I. Averaging with regard to resonance relations between frequencies in oscillatory systems. Ukr Math J 33, 204–208 (1981). https://doi.org/10.1007/BF01086084

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  • DOI: https://doi.org/10.1007/BF01086084

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