This is a preview of subscription content, log in via an institution to check access.
Literature cited
H. Poincaré, New Methods of Celestial Mechanics [Russian translation], Vols. 1–3, Collected Works, Nauka, Moscow (1971).
I. P. Kornfel'd, Ya. G. Sinai, and S. V. Fomin, Ergodic Theory [in Russian], Nauka, Moscow (1980).
S. M. Graff, “On the conservation of hyperbolic tori for Hamiltonian systems,” J. Differ. Equat.,15, No. 1, 1–69 (1974).
A. N. Kolmogorov, “The preservation of conditionally periodic motions under a small change of the Hamiltonian function,” Dokl. Akad. Nauk SSSR,98, No. 4, 527–530 (1954).
V. I. Arnol'd, “A proof of the theorem of A. N. Kolmogorov on the preservation of conditionally periodic motions under a small change of the Hamiltonian function,” Usp. Mat. Nauk,18, No. 6, 91–192 (1963).
Yu. Mozer, “The decomposition of conditionally periodic solutions in converging power series,” Usp. Mat. Nauk,24, No. 2, 165–211 (1969).
D. V. Treshchev, “The mechanism of destruction of resonant tori of Hamiltonian systems,” Mat. Sb.,180, No. 10, 1325–1346 (1989).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 50, No. 4, pp. 123–131, October, 1991.
Rights and permissions
About this article
Cite this article
Treshchev, D.V. Preservation of invariant manifolds of Hamiltonian systems in the presence of a perturbation. Mathematical Notes of the Academy of Sciences of the USSR 50, 1067–1072 (1991). https://doi.org/10.1007/BF01137741
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01137741