RATIONAL LIMIT CYCLES OF ABEL EQUATIONS

被引：3

作者：

Llibre, Jaume ^{[1
]}

Valls, Claudia ^{[2
]}

机构：

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

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

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2021年 / 20卷 / 03期

基金：

欧盟地平线“2020”;

关键词：

Algebraic limit cycles; rational limit cycles; Abel equations; NUMBER; COEFFICIENTS; EXISTENCE;

D O I：

10.3934/cpaa.2021007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We deal with Abel equations dy/dx = A(x)y(2) + B(x)y(3), where A(x) and B(x) are real polynomials. We prove that these Abel equations can have at most two rational limit cycles and we characterize when this happens. Moreover we provide examples of these Abel equations with two nontrivial rational limit cycles.

引用

页码：1077 / 1089

页数：13

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