Liouvillian integrability of the three-dimensional generalized Hénon–Heiles Hamiltonian
Laboratoire de Physique du Solide, Faculté des Sciences Dhar El Mahraz, Université Sidi Mohamed Ben Abdellah, B.P. 1796, 30000, Fez-Atlas, Morocco
2 Laboratoire Systèmes et Environnements Durables, Université Privée de Fès, Lot. Quaraouiyine Route Ain Chkef, 30040, Fez, Morocco
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Accepted: 21 July 2020
Published online: 29 July 2020
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.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2020