ON THE INTEGRABILITY OF POLYNOMIAL VECTOR FIELDS IN THE PLANE BY MEANS OF PICARD-VESSIOT THEORY

被引：11

作者：

Acosta-Humanez, Primitivo B. ^{[1
,2
]}

Tomas Lazaro, J. ^{[3
]}

Morales-Ruiz, Juan J. ^{[4
]}

Pantazi, Chara ^{[3
]}

机构：

[1] Univ Atlantico, Dept Math, Barranquilla, Colombia

[2] Intelectual Co, Barranquilla, Colombia

[3] Univ Politecn Cataluna, Dept Matemat Aplicada 1, Barcelona, Spain

[4] Tech Univ Madrid, Dept Appl Math, Madrid, Spain

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2015年 / 35卷 / 05期

关键词：

Differential Galois theory; Darboux theory of integrability; Poincare problem; rational first integral; integrating factor; Riccati equation; Lienard equation; Liouvillian solution; INVARIANT ALGEBRAIC-CURVES; INVERSE PROBLEMS; DIFFERENTIAL-SYSTEMS; POINCARE PROBLEM; DARBOUX THEORY; 1ST INTEGRALS; FOLIATIONS; EQUATIONS;

D O I：

10.3934/dcds.2015.35.1767

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type foliation. In particular we obtain integrability results for some families of quadratic vector fields, Lienard equations and equations related with special functions such as Hypergeometric and Heun ones. The Poincare problem for some families is also approached.

引用

页码：1767 / 1800

页数：34

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