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V. Arnol’d (1963)
PROOF OF A THEOREM OF A.?N.?KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIANRussian Mathematical Surveys, 18
(1954)
On the Conservation of Conditionally Periodic Motions under Small Perturbation of the Hamiltonian
(1954)
Théorie générale des systèmes dynamiques et mécanique classique (French, 1957)
VI Arnol’d (1963)
Proof of a Theorem by A. N. Kolmogorov on the Invariance of Quasi-Periodic Motions under Small Perturbations of the HamiltonianUspehi Mat. Nauk, 18
J. Moser (1962)
On invariant curves of area-preserving mappings of an anulus
By Kolmogorov, S. Fomin (1961)
Elements of the Theory of Functions and Functional Analysis
V. Arnold, V. Kozlov, A. Neishtadt (1997)
Mathematical aspects of classical and celestial mechanics (2nd ed.)
JK Moser (1962)
Nachr. Akad. Wiss. Göttingen, Math.-Phys. Kl. II
V. Arnold, V. Kozlov, A. Neishtadt (1997)
Mathematical aspects of classical and celestial mechanics
A. Kolmogorov (1954)
On conservation of conditionally periodic motions for a small change in Hamilton's functionProceedings of the USSR Academy of Sciences, 98
Following closely Kolmogorov’s original paper [1], we give a complete proof of his celebrated Theorem on perturbations of integrable Hamiltonian systems by including few “straightforward” estimates.
Regular and Chaotic Dynamics – Springer Journals
Published: Apr 18, 2008
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