In this paper a proof is given of Kolmogorov's theorem on the existence of invariant tori in nearly integrable Hamiltonian systems. The scheme of proof is that of Kolmogorov, the only difference being in the way canonical transformations near the identity are defined. Precisely, use is made of the Lie method, which avoids any inversion and thus any use of the implicit-function theorem. This technical fact eliminates a spurious ingredient and simplifies the establishment of a central estimate.

A proof of Kolmogorov's theorem on invariant tori using canonical transformations defined by the Lie method / G. Benettin, L. Galgani, A. Giorgilli, J.-. Strelcyn. - In: NUOVO CIMENTO. B. - ISSN 0369-3554. - 79:2(1984 Feb 11), pp. 201-223. [10.1007/BF02748972]

A proof of Kolmogorov's theorem on invariant tori using canonical transformations defined by the Lie method

L. Galgani
;
A. Giorgilli
;
1984

Abstract

In this paper a proof is given of Kolmogorov's theorem on the existence of invariant tori in nearly integrable Hamiltonian systems. The scheme of proof is that of Kolmogorov, the only difference being in the way canonical transformations near the identity are defined. Precisely, use is made of the Lie method, which avoids any inversion and thus any use of the implicit-function theorem. This technical fact eliminates a spurious ingredient and simplifies the establishment of a central estimate.
Classical mechanics of discrete systems: general mathematical aspects; Physics and Astronomy (all)
Settore MAT/07 - Fisica Matematica
Settore FIS/05 - Astronomia e Astrofisica
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
11-feb-1984
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/243877
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