Àííîòàöèÿ:
We review Kolmogorov’s 1954 fundamental paper On the persistence of conditionally
periodic motions under a small change in the Hamilton function (Dokl. akad. nauk SSSR,
1954, vol. $\bf 98$, pp. 527–530), both from the historical and the mathematical point of view. In
particular, we discuss Theorem 2 (which deals with the measure in phase space of persistent
tori), the proof of which is not discussed at all by Kolmogorov, notwithstanding its centrality
in his program in classical mechanics.
In Appendix, an interview (May 28, 2021) to Ya. Sinai on Kolmogorov's legacy in classical
mechanics is reported.
Êëþ÷åâûå ñëîâà:
Kolmogorov’s theorem on invariant tori, KAM theory, history of dynamical systems,
small divisors, Hamiltonian systems, perturbation theory, symplectic transformations, nearlyintegrable
systems, measure of invariant tori
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