Lochak P., Neishtadt A. I.
Ecole Normale Superieure, F-75230, Paris, FranceSpace Research Institute, Moscow, 117810, Russia.
Chaos. 1992 Oct;2(4):495-499. doi: 10.1063/1.165891.
A Hamiltonian system differing from an integrable system by a small perturbation equals, similar 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 as varepsilon decreases linearly. If the unperturbed Hamiltonian is a quasiconvex function of these "actions," the changes in them remain small ( equals, similar 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.
分析了一个通过小扰动与可积系统不同的哈密顿系统，其中(\varepsilon)类似。根据涅霍罗舍夫定理，在一个时间间隔内，未受扰动系统的“作用”变量的扰动运动变化很小，该时间间隔的长度随着(\varepsilon)线性减小而指数增加。如果未受扰动的哈密顿量是这些“作用”的拟凸函数，那么在量级为(\exp(const / \varepsilon^{(1/2n)}))的时间间隔内，它们的变化仍然很小（等于，类似(\varepsilon^{(1/2n)})），其中(n)是系统的自由度数量。
