We characterize the families of periodic orbits of two discontinuous piecewise differential systems in [Formula: see text] separated by a plane using their first integrals. One of these discontinuous piecewise differential systems is formed by linear differential systems, and the other by nonlinear differential systems.

中文翻译：

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通过第一积分穿越周期轨道

我们在 [公式：见正文] 中使用它们的第一个积分来表征由平面分隔的两个不连续分段微分系统的周期轨道族。这些不连续的分段微分系统之一由线性微分系统构成，另一个由非线性微分系统构成。