We provide normal forms and the global phase portraits in the Poincaré disk for all planar polynomial vector fields of the form lineal plus cubic homogeneous that are symmetric with respect to the x-axis or to the y-axis and having a nilpotent saddle at the origin.

中文翻译：

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线性加三次齐次多项式可逆矢量场的幂鞍

对于线性和三次同质形式的所有平面多项式矢量场，我们在Poincaré圆盘中提供正态形式和全局相像，这些平面多项式矢量场相对于x轴或y轴对称，并且在原点处具有幂等鞍形。