On the number of limit cycles surrounding a unique singular point for polynomial differential systems of arbitrary degree

被引：4

作者：

Garcia, Belen ^{[1
]}

Llibre, Jaume ^{[2
]}

Perez del Rio, Jesus S. ^{[1
]}

机构：

[1] Univ Oviedo, Dept Matemat, Oviedo 33007, Spain

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

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2008年 / 69卷 / 12期

关键词：

Limit cycle; Bifurcation from a center; Averaging theory;

D O I：

10.1016/j.na.2007.11.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the number of limit cycles that bifurcate from the periodic orbits of the center x(over dot) = -yR(x, y), y(over dot) = xR(x, y) where R is a convenient polynomial of degree 2, when we perturb it inside the class of all polynomial different systems of degree n. We use averaging theory for computing this number. As a consequence of our study we provide the biggest number of limit cycles surrounding a unique singular point in terms of the degree of the system, known up to now. (C) 2007 Elsevier Ltd. All rights reserved.

引用

页码：4461 / 4469

页数：9

共 15 条

[1] BIFURCATION OF LIMIT-CYCLES FROM CENTERS AND SEPARATRIX CYCLES OF PLANAR ANALYTIC SYSTEMS [J].