A dynamical system with a cosymmetry is considered. V. I. Yudovich showed that a noncosymmetric equilibrium of such a system under the conditions of the general position is a member of a one-parameter family. In this paper, it is assumed that the equilibrium is cosymmetric, and the linearization matrix of the cosymmetry is nondegenerate. It is shown that, in the case of an odd-dimensional dynamical system, the equilibrium is also nonisolated and belongs to a one-parameter family of equilibria. In the even-dimensional case, the cosymmetric equilibrium is, generally speaking, isolated. The Lyapunov – Schmidt method is used to study bifurcations in the neighborhood of the cosymmetric equilibrium when the linearization matrix has a double kernel. The dynamical system and its cosymmetry depend on a real parameter. We describe scenarios of branching for families of noncosymmetric equilibria.

考虑具有共对称性的动力系统。VI Yudovich 表明，这种系统在一般位置条件下的非共对称平衡是单参数族的成员。在本文中，假设平衡是共对称的，并且共对称的线性化矩阵是非退化的。结果表明，在奇维动力系统的情况下，平衡也是非孤立的，属于单参数平衡族。在偶数维情况下，共对称平衡一般来说是孤立的。当线性化矩阵具有双核时，Lyapunov-Schmidt 方法用于研究共对称平衡附近的分岔。动力系统及其共对称性取决于实参数。