标题： Poincaré-Dulac正规形式的算法约化及李代数结构 显示英文标题

标题： Algorithmic reduction of Poincare'-Dulac normal forms and Lie algebraic structure

摘要： 给定共振系统的庞加莱-杜拉正常形式通常不是唯一的；给定一个特定的正常形式，人们希望进一步将其简化为最简形式。 在这篇短文中，我们给出了一个算法，基于正常形式集合的李代数结构，以获得这一结果。 该算法可以在某些条件下应用，这些条件虽然非常规但经常出现在实际应用中；当适用时，它只需要求解线性方程，比作者之前的工作中提出的算法 [Lett. Math. Phys. 42, 103-114; 和 Ann. I.H.P. 70, 461-514] 更具威力。 显示英文摘要

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].