Puiseux Integrability of Differential Equations

被引：23

作者：

Demina, Maria, V ^{[1
]}

Gine, Jaume ^{[2
]}

Valls, Claudia ^{[3
]}

机构：

[1] HSE Univ, Dept Appl Math, 34 Tallinskaya St, Moscow 123458, Russia

[2] Univ Lleida, Dept Matemat, Avda Jaume 11,69, Lleida 25001, Spain

[3] Univ Lisbon, Dept Matemat, Inst Super Tecn, Av Rovisco Pais, P-1049001 Lisbon, Portugal

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2022年 / 21卷 / 02期

基金：

俄罗斯科学基金会;

关键词：

Puiseux integrability; Invariant curves; Exponential factors; Polynomial differential systems; Lienard differential equations; INVARIANT ALGEBRAIC-CURVES; LIOUVILLIAN INTEGRABILITY;

D O I：

10.1007/s12346-022-00565-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we study polynomial differential systems in the plane and define a new type of integrability that we call Puiseux integrability. As its name indicates, the Puiseux integrability is based on finding and studying the structure of Puiseux series that are solutions of a first order ordinary differential equation related to the original differential system. The necessary and sufficient conditions to have such integrability are given. These conditions are used to solve the integrability problem for quintic Lienard differential systems with a cubic damping function.

引用

页数：35

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