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

K. Efstathiou, D. A. Sadovskií, R. H. Cushman

Proceedings of the Royal Society A, 459(2040), 2997-3019 (2003)
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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.