Liouvillian integrability of the three-dimensional generalized Hénon–Heiles Hamiltonian

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.