Poincare '-Dulac规范形的数学约化与李代数结构
Algorithmic reduction of Poincare'-Dulac normal forms and Lie algebraic structure
摘要：
一个给定的共振系统的庞加莱-杜拉克规范形式一般是不唯一的;给定一个特定的规范形式，人们希望进一步将其简化为一个最简单的规范形式。在本说明中，我们给出了一个算法，基于李代数结构的规范形式的集合，以获得这一点。该算法可以应用在一些条件下，非通用的，但经常在应用中遇到的，当适用时，它只需要解决线性方程组，并提出了一个更强大的比以前的工作中提出的同一作者[Lett. Math.Phys.42，103-114;和Ann.I.H.P.70，461-514]。
英文摘要：
The Poincare'-Dulac normal form of a given resonant system is in general non unique; given a specific normal form, one would like to further reduce it to a simplest normal form. In this note we give an algorithm, based on the Lie algebraic structure of the set of normal forms, to obtain this. The algorithm can be applied under some condition, non generic but often met in applications; when applicable, it only requires to solve linear equations, and is more powerful than the one proposed in previous work by the same author [Lett. Math. Phys. 42, 103-114; and Ann. I.H.P. 70, 461-514].
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