On equilibrium bifurcations in the cosymmetry collapse of a dynamical system

We study the bifurcations that accompany the collapse of a continuous family of equilibria of a cosymmetric dynamical system (or a family of solutions to a cosymmetric operator equation in general) under some perturbation that destroys cosymmetry. Using the Lyapunov–Schmidt method, we expatiate on the cases in which the branching equation is one- or two-dimensional.