In this paper we focus on a class of symmetric vector fields in the context of singularly perturbed fast-slow dynamical systems. Our main question is to know how symmetry properties of a dynamical system are affected by singular perturbations. In addition, our approach uses tools in geometric singular perturbation theory [8], which address the persistence of normally hyperbolic compact manifolds. We analyse the persistence of such symmetry properties when the singular perturbation parameter \(\varepsilon \) is positive and small enough, and study the existing relations between symmetries of the singularly perturbed system and symmetries of the limiting systems, which are obtained from the limit \(\varepsilon \rightarrow 0\) in the fast and slow time scales. This approach is applied to a number of examples.

在本文中，我们关注奇异摄动快慢动力系统中的一类对称矢量场。我们的主要问题是要知道动力学系统的对称性如何受到奇异摄动的影响。另外，我们的方法使用几何奇异摄动理论中的工具[8]，该工具解决了常双曲紧流形的持久性。我们分析了奇摄动参数\（\ varepsilon \）为正且足够小时这种对称性质的持久性，并研究了奇摄动系统的对称性与极限系统对称性之间的现有关系，该关系可从极限获得\（\ varepsilon \ rightarrow 0 \）在快速和慢速时间范围内。此方法适用于许多示例。