Kolmogorov theorem and classical perturbation theory. (English) Zbl 0886.58098
The authors suggest a new proof of the Kolmogorov-Arnold-Moser theorem which avoids using super fast converging iterations in dealing with small denominators. Instead they consider expansions obtained via the classical perturbation theory and show that the construction of the Kolmogorov normal form can be implemented in such a way that the corresponding series in small parameter will converge.
Reviewer: Yu.Kifer (Jerusalem)
MSC:
| 37J40 | Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion |
| 37J99 | Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems |
| 34C27 | Almost and pseudo-almost periodic solutions to ordinary differential equations |
| 37G05 | Normal forms for dynamical systems |
