This paper deals with the analysis of Hamiltonian Hopf bifurcations in three-degree-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.

本文针对三自由度系统中的哈密顿Hopf分叉进行分析，其对应哈密顿量线性化的频率为\（\ omega：3：6 \）共振（\（\ omega = 1 \）或\（2 \））。我们获得了不可积分的截断的二阶范式，并用减少的相空间的不变性表示。截断的一阶范式生成了一个可积分系统，该系统使用一个单自由度系统进行了分析。在本文中，考虑了一些失谐参数，并找到了非退化哈密顿霍普夫分支。为了研究哈密顿Hopf分支，我们将简化的哈密顿量转换为标准形式。