Kolmogorov's 1954 paper on nearly-integrable Hamiltonian systems

Regular and Chaotic Dynamics

Volumn 13, Issue 2, 2008, Pages 130-139

  Chierchia, Luigi ^a  

^a ROMA TRE UNIVERSITY   (Italy)

Author keywords

Hamiltonian systems; KAM theory; Kolmogorov's theorem; Nearly integrable systems; Perturbation theory; Small divisors; Symplectic transformations

Indexed keywords

EID: 42549087394     PISSN: 15603547     EISSN: 14684845     Source Type: Journal    
DOI: 10.1134/s1560354708020056     Document Type: Review

References (7)

1. Kolmogorov, A.N., On the Conservation of Conditionally Periodic Motions under Small Perturbation of the Hamiltonian, Dokl. akad. nauk SSSR, 1954, vol. 98, pp. 527-530. Engl. transl.: Stochastic Behavior in Classical and Quantum Hamiltonian Systems, Volta Memorial conference, Como, 1977, Lecture Notes in Physics, vol. 93, Springer, 1979, pp. 51-56.
2. Kolmogorov, A.N., Théorie générale des systémes dynamiques et mcanique classique (French, 1957), Proceedings of the International Congress of Mathematicians, Amsterdam, 1954, Vol. 1, pp. 315-333, Erven P. Noordhoff N.V., Groningen; North-Holland Publishing Co., Amsterdam.
3. Arnol'd, V.I., Kozlov, V.V., and Neishtadt, A.I., Mathematical Aspects of Classical and Celestial Mechanics, 3rd ed., Dynamical Systems III, Encyclopaedia of Mathematical Sciences, vol. 3, Berlin: Springer-Verlag, 2006.
4. Arnol'd, V.I., Proof of a Theorem by A. N. Kolmogorov on the Invariance of Quasi-Periodic Motions under Small Perturbations of the Hamiltonian, Uspehi Mat. Nauk, 1963, vol. 18, no. 5(113), pp. 13-40 [Russ. Math. Surv. (Engl. transl.), 1963, vol. 18, no. 5, pp. 9-36.]
5. Moser, J.K., On Invariant Curves of Area-Preserving Mappings of an Annulus, Nachr. Akad. Wiss. Göttingen, Math.-Phys. Kl. II, 1962, pp. 1-20.
6. Moser, J.K., AMS Mathematical Review MR0097598 (20 #4066) of the article [2]
7. Kolmogorov, A.N. and Fomin, S.V., Elements of the Theory of Functions and Functional Analysis, Courier Dover Publications, 1999 [Translated from the original Russian edition (Izdat. Moskov. Univ., Moscow, 1954)].