Non-integrability of a three-dimensional generalized Hénon-Heiles system
Faculty of Mathematics and Informatics, Sofia University, 5 J. Bouchier Blvd., 1164, Sofia, Bulgaria
Accepted: 5 October 2021
Published online: 15 October 2021
In recent paper Fakkousy et al. show that the 3D Hénon-Heiles system with Hamiltonian is integrable in sense of Liouville when ; or , B-arbitrary; or (and of course, when , in which case the Hamiltonian is separable). It is known that the second case remains integrable for A, C, B arbitrary. Using Morales-Ramis theory, we prove that there are no other cases of integrability for this system.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021