Literature cited
N. N. Bogolyubov, Yu. A. Mitropol'skii, and A. M. Samoilenko, The Method of Accelerated Convergence in Nonlinear Mechanics [in Russian], Naukova, Dumka, Kiev (1969).
A. M. Samoilenko, “On the conservation of an invariant torus under perturbations,” Izv. Akad. Nauk SSSR, Ser. Mat., No.34, 1219–1241 (1970).
A. M. Samoilenko, “On the exponential stability of an invariant torus of a dynamical system,” Differents. Uravn.,11, No. 5, 820–834 (1978).
A. M. Samoilenko, “On the reduction of a dynamical system to canonical form in the neighborhood of a smooth invariant torus,” Izv. Akad. Nauk SSSR, Ser. Mat., No. 36, 209–233 (1972).
M. Reed and B. Simon, Methods of Modern Mathematical Physics, Academic Press, New York-London (1972).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 37, No. 6, pp. 751–756, November–December, 1985.
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Samoilenko, A.M., Svishchuk, M.Y. Splitting of a system of differential equations with slowly varying phase in the neighborhood of an asymptotically stable invariant torus. Ukr Math J 37, 617–621 (1985). https://doi.org/10.1007/BF01057431
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DOI: https://doi.org/10.1007/BF01057431