In this paper, a new bifurcation phenomenon of nilpotent singular point is analyzed. A nilpotent focus or center of the planar systems with 3-multiplicity can be broken into two complex singular points and a second order elementary weak focus. Then, two more limit cycles enclosing the second order elementary weak focus can bifurcate through the multiple Hopf bifurcation.

中文翻译：

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幂零焦点的新双分岔

本文分析了幂等奇异点的一种新的分岔现象。具有 3 重数的平面系统的幂零焦点或中心可以分解为两个复奇异点和一个二阶基本弱焦点。然后，包含二阶基本弱焦点的另外两个极限环可以通过多次 Hopf 分岔进行分岔。