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Estimates of stability time for nearly integrable systems with a quasiconvex Hamiltonian. (English) Zbl 1055.37573

Summary: A Hamiltonian system differing from an integrable system by a small perturbation \(\sim\varepsilon\) is analyzed. According to the Nekhoroshev theorem, the changes in the perturbed motion of the “action” variables of the unperturbed system are small over a time interval which increases exponentially in length \(\varepsilon\) as decreases linearly. If the unperturbed Hamiltonian is a quasiconvex function of these “actions,” the changes in them remain small \((\sim\varepsilon^{1/2n})\) over a time interval on the order of exp(const/\(\varepsilon^{1/2n})\), where \(n\) is the number of degrees of freedom of the system.

MSC:

37J25 Stability problems for finite-dimensional Hamiltonian and Lagrangian systems
70H08 Nearly integrable Hamiltonian systems, KAM theory
37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
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References:

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