微分伽罗瓦论与李对称
Differential Galois Theory and Lie Symmetries
摘要：
本文研究了线性微分方程系统的无穷小对称的微分伽罗瓦群和李代数之间的相互作用。我们表明，一些对称性可以被看作是解决方案的一个层次的线性微分系统。我们证明了有理对称的存在性约束了系统中的微分伽罗瓦群，这种约束依赖于对称性沿零解的麦克劳林级数。
英文摘要：
We study the interplay between the differential Galois group and the Lie algebra of infinitesimal symmetries of systems of linear differential equations. We show that some symmetries can be seen as solutions of a hierarchy of linear differential systems. We show that the existence of rational symmetries constrains the differential Galois group in the system in a way that depends of the Maclaurin series of the symmetry along the zero solution.
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