For the space of single-variable monic and centered complex polynomial vector fields of arbitrary degree d, it is proved that any bifurcation which preserves the multiplicity of equilibrium points admits a decomposition into a finite number of elementary bifurcations, and the elementary bifurcations are characterized.

中文翻译：

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复多项式矢量场的保重性全局分支的刻画

对于任意变量d的单变量单调和中心复多项式矢量场的空间，证明了任何保留了多个平衡点的分叉都允许分解为有限数量的基本分叉，并且对基本分叉进行了表征。