Hopf-takens bifurcations and centres

被引：23

作者：

Caubergh, M ^{[1
]}

Dumortier, F ^{[1
]}

机构：

[1] Limburgs Univ Ctr, B-3590 Diepenbeek, Belgium

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2004年 / 202卷 / 01期

关键词：

Hopf singularity; centers; limit cycles; generic bifurcation diagrams; normal forms; lyapunov coefficients; bautin ideal; Melnikov functions;

D O I：

10.1016/j.jde.2004.03.018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The paper deals with Hopf-Takens bifurcations, both in generic families and in families containing centres. Attention goes to the relation between normal forms, Lyapunov coefficients and the Bautin ideal. In case the Bautin ideal has only one generator we pay attention to the first non-zero Melnikov function. (C) 2004 Elsevier Inc. All rights reserved.

引用

页码：1 / 31

页数：31

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