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

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dc.contributor.authorStachowiak, Tomasz
dc.contributor.authorMaciejewski, Andrzej J.
dc.date.accessioned2025-12-30T15:53:36Z
dc.date.issued2021
dc.description.abstractThe 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 integrable due to the lack of additional meromorphic first integrals. We prove that the analog of the two-body problem on the Heisenberg group is not integrable in the Liouville sense.
dc.description.sponsorshipWe would like to thank the anonymous referees for helping to improve the manuscript. This work has been supported by grants No. DEC-2011/02/A/ST1/00208 and DEC-2013/09/B/ST1/04130 of the National Science Centre of Poland. For the second author, this research was partially supported by the National Science Center of Poland Under Grant No. 2020/39/D/ST1/01632.
dc.identifier.citationNon-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
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2021.074
dc.identifier.issn1815-0659
dc.identifier.other2020 Mathematics Subject Classification: 37J30; 70F05; 70H07; 70G45; 53C17
dc.identifier.otherarXiv:2103.10495
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/211349
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titleNon-Integrability of the Kepler and the Two-Body Problems on the Heisenberg Group
dc.typeArticle

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Symmetry, Integrability and Geometry: Methods and Applications, 2021, том 17, випуск за цей рік