Using the Euler–Jacobi formula there is a relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for the polynomial differential systems $$\dot{x}=P(x,y)$$ x ˙ = P ( x , y ) , $$\dot{y} =Q(x,y)$$ y ˙ = Q ( x , y ) with degree of P equal to 2 and degree of Q equal to m when these systems have 2 m finite singular points.

中文翻译：

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度数 (2, m) 的平面多项式微分系统的拓扑索引的配置

使用 Euler-Jacobi 公式，多项式向量场的奇异点与其拓扑指数之间存在关系。使用这个公式，我们获得多项式微分系统的奇异点的配置及其拓扑指数 $$\dot{x}=P(x,y)$$x ˙ = P ( x , y ) , $$\ dot{y} =Q(x,y)$$ y ˙ = Q ( x , y ) 当这些系统有 2 m 个有限奇异点时，P 的次数等于 2，Q 的次数等于 m。