Abstract

For systems of ordinary differential equations (ODEs) with a nondegenerate linear part in the general and Hamiltonian cases, the problem of finding invariant coordinate subspaces in the coordinates of the normal form calculated in the vicinity of the equilibrium is stated. Conditions for the existence of such invariant subspaces in terms of the resonant relations between the eigenvalues of the linear part of the system are obtained. An algorithm for finding the resonant relations between the eigenvalues without their explicit calculation is described; this algorithm substantially uses computer algebra methods and the q-analog of the polynomial subresultants. The implementation of this algorithm in three popular computer algebra systems—Mathematica, Maple, and SymPy—is discussed. Interesting model examples are provided.

中文翻译：

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一类常微分方程组正规形的不变坐标子空间。

摘要

对于在一般情况和哈密顿情况下具有非退化线性部分的常微分方程组（ODE），提出了在平衡附近计算的法线形式的坐标中找到不变坐标子空间的问题。根据系统线性部分的特征值之间的共振关系，获得了此类不变子空间存在的条件。描述了一种无需特征值即可找到特征值之间共振关系的算法；该算法主要使用计算机代数方法和多项式子结果的q模拟。该算法在三种流行的计算机代数系统（Mathematica，Maple）中的实现和SymPy —进行了讨论。提供了有趣的模型示例。