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
收藏
页码：2657 / 2661
页数：5
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