具有一个快相和小振幅的哈密顿系统的平均化
On Averaging for Hamiltonian Systems with One Fast Phase and Small Amplitudes
摘要：
许多文献从不同的角度考虑了具有一个快相的系统的平均问题。Krylov和Bogolyubov的平均方法和KAM理论的方法起源于这条研究路线，Neishtadt获得了最完整的结果，其中系数假定为实解析。然而，在许多问题，这是有趣的从应用的角度来看，解析相关性停止举行的邻域中的一些点。我们表明，人们可以选择一个变换，这样的平均程序Neishtadt是适用于这些地区和这样的通道限制是统一的。
英文摘要：
The problem of averaging for systems with one fast phase was considered from various points of view in many papers. The averaging method of Krylov and Bogolyubov and methods of KAM theory originated this line of research, the most complete results were obtained by Neishtadt, where the coefficients are assumed real analytic. However, in many problems which are interesting from the point of view of applications, analytic dependence ceases to hold in the neighborhoods of some points. We show that one can choose a transformation such that the averaging procedure of Neishtadt is applicable in these neighborhoods and such passage to limit is uniform.
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