- 02-297 Sevryuk M.B.
- The classical KAM theory at the dawn of the twenty-first century
Jul 8, 02
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Abstract. We survey several recent achievements in the 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 the weak
nondegeneracy conditions, Gevrey smoothness of families of perturbed
invariant tori, the ``exponential condensation'' of perturbed tori,
destruction mechanisms of the resonant unperturbed tori, the 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. The paper contains 152 references.