# Linear Hamiltonian Hopf bifurcation for point-group-invariant perturbations of the 1:1:1 resonance

### Abstract

We consider $G times R$-invariant Hamiltonians $H$ on complex projective $2$-space, where $G$ is a point group and $R$ is the time-reversal group. We find the symmetry-induced stationary points of $H$ and classify them in terms of their linear stability. We then determine those points that can undergo a linear Hamiltonian Hopf bifurcation.