Let $\dot{x}=P(x,y)$, $\dot{y}=Q(x,y)$ be a differential system with P and Q real polynomials, and let $d=\max \{\text{deg}P,\text{deg}Q\}$. A singular point p of this differential system is a global center if ${\mathbb{R}}^2\setminus \{p\}$ is filled with periodic orbits. We prove that if d is even then the polynomial differential systems have no global centers.

中文翻译：

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偶数次多项式微分系统没有全局中心

让 $\dot{X}=P（X，ÿ）$， $\dot{ÿ}=问（X，ÿ）$是具有P和Q实多项式的微分系统，$d=\mathrm{最大限度}\{\text{度}P，\text{度}问\}$。如果该微分系统的奇异点p为全局中心，则${\mathbb{[R}}^{\mathrm{2个}}\setminus \{p\}$充满了周期性的轨道。我们证明，如果d是偶数，则多项式微分系统就没有全局中心。