Literature cited
N. N. Bogolyubov, Some Statistical Methods in Mathematical Physics [in Russian], Academy of Sciences of the Ukrainian SSR, Lvov (1945).
N. N. Bogolyubov and Yu. A. Mitropol'skii, “Method of integral manifolds in nonlinear mechanics,” Proc. Internat. Sympos. Nonlinear Vibrations, Academy of Sciences of the Ukrainian SSR, Kiev,1, 93–154 (1963).
Yu. A. Mitropol'skii.and O. B. Lykova, Integral Manifolds in Nonlinear Mechanics [in Russian], Nauka, Moscow (1973).
Ya. S. Baris and O. B. Lykova, “Asymptotic expansions of invariant manifolds. I,” Ukr, Mat. Zh.,39, No. 4, 411–418 (1987).
A. M. Lyapunov, The General Problem of Stability of Motion, GITTL, Moscow-Leningrad (1950).
O. B. Lykova, “Behavior of solutions of a system of differential equations in the neighborhood of an isolated statistical solution,” Dokl. Akad. Nauk SSSR,115, No. 3, 447–449 (1957).
A. Kelley, “The stable, center-stable, center, center-unstable, unstable manifolds,” J. Diff. Eq.,3, 546–570 (1967).
N. Bourbaki, Functions of a Real Variable [Russian translation], Nauka, Moscow (1965).
Ya. S. Baris and O. B. Lykova, “Approximate integral manifolds of systems of differential equations,” Preprint, Academy of Sciences of the Ukrainian SSR, Institute of Mathematics, 79.15, Kiev (1979).
Ya. S. Baris and O. B. Lykova, “Approximate integral manifolds of systems of linear differential equations,” Preprint, Academy of Sciences of the Ukrainian SSR, Institute of Mathematics, 80.5, Kiev (1980).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 40, No. 6, pp.709–716, November–December, 1988.
Rights and permissions
About this article
Cite this article
Baris, Y.S., Lykova, O.B. Asymptotic expansions of invariant manifolds. II. Ukr Math J 40, 597–603 (1988). https://doi.org/10.1007/BF01057176
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01057176