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References (10)
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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
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(1954)
On the Conservation of Conditionally Periodic Motions under Small Perturbation of the Hamiltonian -
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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
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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.) -
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V. Arnold, V. Kozlov, A. Neishtadt (1997)
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A. Kolmogorov (1954)
On conservation of conditionally periodic motions for a small change in Hamilton's functionProceedings of the USSR Academy of Sciences, 98
- Publisher
- Springer Journals
- Copyright
- Copyright © 2008 by MAIK Nauka
- Subject
- Mathematics; Dynamical Systems and Ergodic Theory
- ISSN
- 1560-3547
- eISSN
- 1468-4845
- DOI
- 10.1134/S1560354708020056
- Publisher site
- See Article on Publisher Site
Abstract
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.
Journal
Regular and Chaotic Dynamics – Springer Journals
Published: Apr 18, 2008