ANALYTIC INTEGRABILITY OF A CLASS OF PLANAR POLYNOMIAL DIFFERENTIAL SYSTEMS

被引：1

作者：

Llibre, Jaume ^{[1
]}

Valls, Claudia ^{[2
]}

机构：

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

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

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2015年 / 20卷 / 08期

关键词：

Planar polynomial systems; quasi homogeneous polynomial differential systems; analytic first integrals; pseudo meromorphic first integrals; 1ST INTEGRALS;

D O I：

10.3934/dcdsb.2015.20.2657

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we find necessary and sufficient conditions in order that the differential systems of the form (x) over dot = x f(y), (y) over dot = g(y), with f and g polynomials, have a first integral which is analytic in the variable x and meromorphic in the variable y. We also characterize their analytic first integrals in both variables x and y. These polynomial differential systems are important because after a convenient change of variables they contain all quasi homogeneous polynomial differential systems in R-2.

引用

页码：2657 / 2661

页数：5

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