Non-Integrability of the Kepler and the Two-Body Problems on the Heisenberg Group
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Published:2021-07-31
Issue:
Volume:
Page:
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ISSN:1815-0659
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Container-title:Symmetry, Integrability and Geometry: Methods and Applications
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language:
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Short-container-title:SIGMA
Author:
Stachowiak Tomasz, ,Maciejewski Andrzej J., , ,
Abstract
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 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.
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
Subject
Geometry and Topology,Mathematical Physics,Analysis
Cited by
1 articles.
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