The method of accelerated convergence in problems of non-linear mechanics

1 Krylov, N. M.; Bogoliubov, N. N. Méthodes de la mécanique non linéaire appliquées à l'étude des oscillations stationnaires Izd. AN USSR 1934 (Russian)

2 Kolmogorov, A. N. On conservation of conditionally periodic motions for a small change in Hamilton's function DAN SSSR 98 1954 527-530 (Russian) MR0068687

3 Arnold, V. I. Small denominators. I. Mapping the circle onto itself Izvestiya AN SSSR 25 1961 21-86 (Russian) MR0140699

4 Arnold, V. I. Proof of a theorem of A. N. Kolmogorov on the preservation of conditionally periodic motions under a small perturbation of the Hamiltonian UMN 18 1963 13-40 (Russian) MR0163025

5 Bogoliubov, N. N. Quasiperiodic solutions in problems of nonlinear mechanics Izd. "Naukova Dumka" 1 1964 11-101 (Russian) MR0209571

6 Bogoliubov, N. N., Theory of turbulance for nonlinear maechanics, Collected works: Institute of construction mechanics, AN USSR, No. 14 (1950), 9-34 (Russian)

7 Bogoliubov, N. N.; Mitropolsky, Y. A. Régimes Quasi-Périodiques dans les Systèmes Oscillants non linéaires Les Vibrations Forcées dans les Systèmes Non-linéaires, Paris VII 1965 193-204

8 Bogoliubov, N. N.; Mitropolsky, Y. A. Asymptotic methods in the theory of non-linear oscillations Fizmatgiz 1963 (Russian) MR0158130 9 Krylov, N. M.; Bogoliubov, N. N. Sur quelques développments formels en séries dans la mécanique non linéaire Vid. AN URSR 1934 (Ukrainian)

10 Bogoliubov, N. N.; Mitropolsky, Y. A. The method of integral manifolds in non-linear mechanics Proc. Internat. Sympos. Non-linear Vibrations 1 1963 93-154 (Russian) MR0162033

11 Mitropolsky, Y. A. Construction of the general solution of non-linear differential equations by a method providing accelerated convergence UMŽ 16 1964 475-501 (Russian) MR0173817

12 Kolmogorov, A. N. On dynamical systems with an integral invariant on the torus DAN SSSR 93 1953 763-766 (Russian) MR0062892

13 Belaga, E. G. The reducibility of a system of ordinary differential equations in the neighborhood of a conditionally periodic motion DAN SSSR 143 1962 255-258 (Russian) MR0138845

14 Moser, J. A new technique for the construction of solutions of nonlinear differential equations Proc. Nat. Acad., U. S. A. 47 1961 1824-1831 MR0132859

15 Moser, J. On invariant curves of area-preserving mappings of an annulus Matem. 6 1962 51-67 (Russian)

16 Nash, Y. The imbedding problem for Riemannian manifolds Ann. Math. 63 1956 20-63 MR0075639

17 Poincaré, H. Les métodes nouvelles de la mecanique celeste, I Paris 1892

18 Denjoy, A. Sur les courbes définies par les équations différentiallesà la surface du tore J. Math. II 1932

19 Mitropolsky, Y. A.; Samoilenko, A. M. On the structure of trajectories on toroidal manifolds Dopovidi AN URSR 8 1964 984-986 (Ukrainian) MR0183948

20 Samoilenko, A. M. On the structure of trajectories on the torus UMŽ 16 1964 769-782 (Russian) MR0183949

21 Lykova, O. B. Quasi-periodic solutions of a nearly canonical system UMŽ 16 1964 752-768 (Russian) MR0190446

22 Mitropolsky, Y. A.; Lykova, O. B. Sur l'existence de Solutions Quasi-périodiques d'un Système Canonique Trouble les Vibrations Forcées dans les Systèmes Non-linéaires, Paris, VII 1965 415-424

23 Mitropolsky, Y. A.; Samoilenko, A. M. On constructing solutions of linear differential equations with quasiperiodic coefficients by the method of improved convergence UMŽ 17 1965 42-59 (Russian) MR0197831

24 Shtokalo, I. Z. A stability and instability criteria for solutions of linear differential equations with quasi-periodical coefficients Matem. Sb. 19 1946 263-286 (Russian) MR0018778

25 Gel'man, A. E. On the reducibility of systems with a quasiperiodic matrix Differencial'nye Uravnenija 1 1965 283-294 (Russian) MR0208034

26 Adrianova, L. Ja. The reducibility of systems of $n$ linear differential equations with quasi-periodic coefficients Vest. LGU 17 1962 14-24 (Russian) MR0139779

27 Blinov, I. N. Analytic representation of the solution of a system of linear differential equations with almost periodic coefficients which depend on a parameter Differencial'nye Uravnenija 1 1965 1042-1053 (Russian) MR0196191

28 Arnold, V. I. Small denominators and problems of stability of motion in classical and celestial mechanics UMN 18 1963 91-192 (Russian) MR0170705

29 Arnold, V. I. Applicability conditions and an error bound for the averaging method for systems in the process of evolution through a resonance DAN SSSR 161 1965 9-12 (Russian) MR0170705

30 Arnold, V. I. Stability and instability in classical mechanics Naukova Dumka, Kiev 1965 85-119 (Russian) MR0193797