Non-Integrability of the Kepler and the Two-Body Problems on the Heisenberg Group

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2021
• Main Authors: Stachowiak, Tomasz, Maciejewski, Andrzej J.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2021
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211349
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Non-Integrability of the Kepler and the Two-Body Problems on the Heisenberg Group. Tomasz Stachowiak and Andrzej J. Maciejewski. SIGMA 17 (2021), 074, 12 pages

The analog of the Kepler system defined on the Heisenberg group introduced by Montgomery and Shanbrom in [Fields Inst. Commun., Vol. 73, Springer, New York, 2015, 319-342, arXiv:1212.2713] is integrable on the zero level of the Hamiltonian. We show that in all other cases the system is not Liouville...