Nondegenerate Hamiltonian Hopf Bifurcations in $\omega : 3 : 6$ Resonance $(\omega = 1$ or $2)$

This paper deals with the analysis of Hamiltonian Hopf bifurcations in threedegree-
of-freedom systems, for which the frequencies of the linearization of the corresponding
Hamiltonians are in $\omega : 3 : 6$ resonance $(\omega = 1$ or $2)$. We obtain the truncated second-order
normal form that is not integrable and expressed in terms of the invariants of the reduced
phase space. The truncated first-order normal form gives rise to an integrable system that is
analyzed using a reduction to a one-degree-of-freedom system. In this paper, some detuning
parameters are considered and nondegenerate Hamiltonian Hopf bifurcations are found. To
study Hamiltonian Hopf bifurcations, we transform the reduced Hamiltonian into standard
form.