The Completely Integrable Differential Systems are Essentially Linear Differential Systems

被引：12

作者：

Llibre, Jaume ^{[1
]}

Valls, Claudia ^{[2
]}

Zhang, Xiang ^{[3
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, Spain

[2] Univ Tecn Lisboa, Inst Super Tecn, Dept Matemat, P-1049001 Lisbon, Portugal

[3] Shanghai Jiao Tong Univ, Dept Math, MOE LSC, Shanghai 200240, Peoples R China

来源：

JOURNAL OF NONLINEAR SCIENCE | 2015年 / 25卷 / 04期

关键词：

Differential systems; Completely integrability; Orbital equivalence; Normal form; Jacobian multiplier; Polynomial differential systems; DARBOUX INTEGRABILITY;

D O I：

10.1007/s00332-015-9243-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let be a autonomous differential system with defined in an open subset of . Assume that the system is completely integrable, i.e., there exist functionally independent first integrals of class with . As we shall see, we can assume without loss of generality that the divergence of the system is not zero in a full Lebesgue measure subset of . Then, any Jacobian multiplier is functionally independent of the first integrals. Moreover, the system is orbitally equivalent to the linear differential system in a full Lebesgue measure subset of . Additionally, for integrable polynomial differential systems, we characterize their type of Jacobian multipliers.

引用

页码：815 / 826

页数：12

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