Abstract

A perturbed Hamiltonian system with a time-independent unperturbed part and a time-periodic perturbation is considered near a stationary solution. First, the normal form of an autonomous Hamiltonian function is recalled. Then the normal form of a periodic perturbation is described. This form can always be reduced to an autonomous Hamiltonian function, which makes it possible to compute local families of periodic solutions of the original system. First approximations of some of these families are found by computing the Newton polyhedron of the reduced normal form of the Hamiltonian function. Computer algebra problems arising in these computations are briefly discussed.

中文翻译：

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具有周期摄动的哈密顿系统的范式

摘要

在固定解附近考虑了具有时间独立无扰动部分和时间周期摄动的摄动哈密顿系统。首先，回想起哈密顿函数的正常形式。然后描述周期扰动的正常形式。这种形式总是可以简化为自治哈密顿函数，从而可以计算原始系统的周期解的局部族。通过计算哈密顿函数的简正形式的牛顿多面体，可以找到其中一些族的第一近似值。简要讨论了这些计算中出现的计算机代数问题。