Degenerate Hopf bifurcation in the presence of symmetry (Q1102594)

The authors analyze a bifurcation problem \({\overset \circ x} = f(x,\lambda)\), \(x\in {\mathbb{R}}^ 4,\) equivariant with respect to a certain 16-element group. The equivariance forces two equal pairs of complex conjugate eigenvalues to cross the imaginary axis simultaneously. The authors find several families of bifurcating time-periodic solutions and discuss their symmetry and stability.