For the double Hamiltonian Hopf bifurcation, the fourth-order truncated normal form reduces to a two-degree-of-freedom system that is non-integrable for almost all coefficient values.
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Double Hamiltonian Hopf Bifurcation: normalization and normal form non-integrability
For the double Hamiltonian Hopf bifurcation, the fourth-order truncated normal form reduces to a two-degree-of-freedom system that is non-integrable for almost all coefficient values.