Hopf-Takens bifurcations and centres

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• 作者：Caubergh ; M. ; Dumortier ; F.
• 关键词：Hopf singularity ; Centers ; Limit cycles ; Generic bifurcation diagrams ; Normal forms ; Lyapunov coefficients ; Bautin ideal ; Melnikov functions
• 刊名：Journal of Differential Equations
• 出版年：2004
• 期刊代码：74_00220396
• 类别：mt
• 出版时间：July 15, 2004
• 卷：202
• 期：1
• 页码：1-31
• 文件大小：362 K

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.