Differential Galois Theory and Lie Symmetries

被引：1

作者：

Blazquez-Sanz, David ^{[1
]}

Morales-Ruiz, Juan J. ^{[2
]}

Weil, Jacques-Arthur ^{[3
]}

机构：

[1] Univ Nacl Colombia, Bogota, Colombia

[2] Univ Politecn Madrid, E-28040 Madrid, Spain

[3] Univ Limoges, F-87065 Limoges, France

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2015年 / 11卷

关键词：

linear differential system; Picard-Vessiot theory; differential Galois theory; infinitesimal symmetries; EQUATIONS; SYSTEMS;

D O I：

10.3842/SIGMA.2015.092

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页数：17

共 22 条

[1]

[Anonymous], 1986, APPL LIE GROUPS DIFF

[2]

[Anonymous], GRUNDLEHREN MATH WIS

[3] Symmetries of linear ordinary differential equations [J].