ALGEBRAIC LIMIT CYCLES FOR QUADRATIC POLYNOMIAL DIFFERENTIAL SYSTEMS

被引：4

作者：

Llibre, Jaume ^{[1
]}

Valls, Claudia ^{[2
]}

机构：

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

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

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2018年 / 23卷 / 06期

关键词：

Algebraic limit cycle; quadratic polynomial differential system; quadratic polynomial vector field; CURVES; INTEGRALS; EXISTENCE;

D O I：

10.3934/dcdsb.2018070

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that for a quadratic polynomial differential system having three pairs of diametrally opposite equilibrium points at infinity that are positively rationally independent, has at most one algebraic limit cycle. Our result provides a partial positive answer to the following conjecture: Quadratic polynomial differential systems have at most one algebraic limit cycle.

引用

页码：2475 / 2485

页数：11

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