In this paper, we report about three cases of integrability in sense of Liouville for three-dimensional generalized Hénon–Heiles Hamiltonian. This also allow to get explicitly integrals of motions for each case. On the other hand, this paper investigates the phase space structure numerically with Poincaré surfaces of section and 3D projections which allow to verify that the analytical results are in agreement with the computations.

中文翻译：

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三维广义Hénon-Heiles哈密顿量的Liouvillian可积性

在本文中，我们报告了关于三维广义Hénon–Heiles哈密顿量在Liouville意义上的三种可积性情况。这也允许为每种情况明确获得运动的积分。另一方面，本文用截面和3D投影的庞加莱表面数值研究了相空间结构，这可以验证分析结果与计算结果是否一致。