Motivated by the definition of rigid centres for planar differential systems, we introduce the study of rigid centres on the center manifolds of differential systems on $\mathbb {R}^{3}$. On the plane, these centres have been extensively studied and several interesting results have been obtained. We present results that characterize the rigid systems on $\mathbb {R}^{3}$ and solve the centre-focus problem for several families of rigid systems.

中文翻译：

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三维微分系统中心流形上的刚心

受平面微分系统刚心定义的启发，我们介绍了在$\mathbb {R}^{3}$上的微分系统中心流形上的刚心研究。在飞机上，这些中心已经被广泛研究，并获得了一些有趣的结果。我们提出了表征$\mathbb {R}^{3}$上的刚性系统的结果，并解决了几个刚性系统家族的中心焦点问题。