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Perturbation of a stable invariant torus of a dynamical system

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Literature cited

  1. N. N. Bogolyubov and Yu. A. Mitropol'skii, “Method of integral manifolds in nonlinear mechanics,” Proc. Internat. Symp. Nonlinear Oscillations [in Russian], Izd. Inst. Matem. AN UkrSSR, Kiev (1963).

    Google Scholar 

  2. Ya. Kurtsveil', “Invariant manifolds of differential systems,” Diff. Urav.,4, No. 5 (1968).

  3. Yu. A. Mitropol'skii and O. B. Lykova, Lectures on the Method of Integral Manifolds [in Russian], Naukova Dumka, Kiev (1968).

    Google Scholar 

  4. Yu. Mozer, “Rapidly-converging iteration method and nonlinear differential equations,” Usp. Matem. Nauk,23, No. 4 (142) (1968).

  5. R. Sacker, “A new approach to the perturbations theory of invariant surfaces,” Commun. Pure Appl. Math.,18, No. 4 (1965).

  6. A. M. Samoilenko, “Perturbation theory of invariant manifolds of a dynamical system,” Proc. Fifth Internat. Conf. Nonlinear Oscillations [in Russian], Izd. Inst. Matem. AN UkrSSR, Kiev (1969).

    Google Scholar 

  7. A. M. Samoilenko, “Conservation of an invariant torus under perturbation,” Izv. Akad. Nauk SSSR, Ser. Matem.,34, No. 6 (1970).

  8. J. K. Hale, Oscillations in Nonlinear Systems, McGraw-Hill, New York (1963).

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 23, No. 1, pp. 130–137, January–February, 1971.

The author is deeply grateful to A. M. Samoilenko for stating the problem and for valuable consultations.

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Golets, V.L. Perturbation of a stable invariant torus of a dynamical system. Ukr Math J 23, 117–123 (1971). https://doi.org/10.1007/BF01086600

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