https://doi.org/10.1140/epjp/s13360-021-02044-0
Regular Article
Non-integrability of a three-dimensional generalized Hénon-Heiles system
Faculty of Mathematics and Informatics, Sofia University, 5 J. Bouchier Blvd., 1164, Sofia, Bulgaria
Received:
23
March
2021
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
