We provide a general method for identifying real quadratic polynomial dynamical systems that can be transformed to symmetric ones by a bijective polynomial map of degree one, the so-called affine map. We mainly focus on symmetry groups generated by rotations, in other words, we treat equivariant and reversible equivariant systems. The description is given in terms of affine varieties in the space of parameters of the system. A general algebraic approach to find subfamilies of systems having certain symmetries in polynomial differential families depending on many parameters is proposed and computer algebra computations for the planar case are presented.

中文翻译：

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关于二次系统的一些对称性

我们提供了一种通用的方法来识别实二次多项式动力系统，该系统可以通过一次双射多项式映射（即所谓的仿射映射）转换为对称系统。我们主要关注由旋转产生的对称群，换句话说，我们处理等变和可逆等变系统。描述是根据系统参数空间中的仿射变异给出的。提出了根据许多参数在多项式微分族中找到具有某些对称性的系统的子族的一般代数方法，并提出了平面情况的计算机代数计算。