|
This article is cited in 45 scientific papers (total in 45 papers)
The classical KAM theory at the dawn of the twenty-first century
M. B. Sevryuk Institute of Energy Problems of Chemical Physics, Russian Academy of Sciences
Abstract:
We survey several recent achievements in KAM theory. The achievements chosen pertain to Hamiltonian systems only and are closely connected with the content of Kolmogorov's original theorem of 1954. They include weak non-degeneracy conditions, Gevrey smoothness of families of perturbed invariant tori, “exponential condensation” of perturbed tori, destruction mechanisms of resonant unperturbed tori, excitation of the elliptic normal modes of the unperturbed tori, and “atropic” invariant tori (i.e., tori that are neither isotropic nor coisotropic). The exposition is informal and nontechnical, and, as a rule, the methods of proofs are not discussed.
Key words and phrases:
KAM theory, Hamiltonian systems, invariant tori, quasi-periodic motions.
Received: June 22, 2002; in revised form October 22, 2002
Citation:
M. B. Sevryuk, “The classical KAM theory at the dawn of the twenty-first century”, Mosc. Math. J., 3:3 (2003), 1113–1144
Linking options:
https://www.mathnet.ru/eng/mmj124 https://www.mathnet.ru/eng/mmj/v3/i3/p1113
|
Statistics & downloads: |
Abstract page: | 712 | References: | 127 |
|