A Note on the Triple-Zero Linear Degeneracy: Normal Forms, Dynamical and bifurcation Behaviors of an Unfolding

A Note on the Triple-Zero Linear Degeneracy: Normal Forms, Dynamical and bifurcation Behaviors of an Unfolding
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DOI：
10.1142/s0218127402006175
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发表时间：
2002-12
期刊：
Int. J. Bifurc. Chaos
影响因子：
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通讯作者：
E. Freire;E. Gamero;A. Rodríguez-Luis;A. Algaba
E. Freire;E. Gamero;A. Rodríguez-Luis;A. Algaba
中科院分区：
其他
文献类型：
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作者：
E. Freire;E. Gamero;A. Rodríguez-Luis;A. Algaba

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本文致力于分析对应于三零特征值的线性简并性的三参数展开中的分岔。我们对余维平衡的两个局部分岔（Takens-Bogdanov 和 Hopf-zero）进行了研究，并证明它们是非简并的。这可以证明几种周期性轨道分岔（二级霍普夫，……）和全局现象（同宿、异宿）的存在。所得结果应用于Rossler方程的研究。
This paper is devoted to the analysis of bifurcations in a three-parameter unfolding of a linear degeneracy corresponding to a triple-zero eigenvalue. We carry out the study of codimension-two local bifurcations of equilibria (Takens–Bogdanov and Hopf-zero) and show that they are nondegenerate. This allows to put in evidence the presence of several kinds of bifurcations of periodic orbits (secondary Hopf,…) and of global phenomena (homoclinic, heteroclinic). The results obtained are applied in the study of the Rossler equation.