Abstract In this paper, complete integrability and linearizability of cubic Z 2 systems with two non-resonant and elementary singular points are investigated. First of all, four simple normal forms are obtained based on the coefficients and eigenvalues of cubic Z 2 systems. Then, the integrable and linearizable conditions are classified according to the four different cases respectively, and the problem is solved thoroughly for cubic Z 2 systems with two non-resonant singular points.

中文翻译：

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具有非共振奇异点的三次 Z2 系统的可积性和线性化

摘要 本文研究了具有两个非共振和初等奇异点的三次Z 2 系统的完全可积性和线性化性。首先，根据三次Z 2 系统的系数和特征值，得到四种简单的范式。然后，分别根据四种不同情况对可积条件和可线性化条件进行分类，彻底解决了具有两个非共振奇异点的三次Z 2 系统的问题。