An Infinite Family of Maximally Superintegrable Systems in a Magnetic Field with Higher Order Integrals
We construct an additional independent integral of motion for a class of three-dimensional minimally superintegrable systems with a constant magnetic field. This class was introduced in [J. Phys. A: Math. Theor. 50 (2017), 245202, 24 pages] and it is known to possess periodic closed orbits. In the p...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2018 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209865 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | An Infinite Family of Maximally Superintegrable Systems in a Magnetic Field with Higher Order Integrals / A. Marchesiello, L. Šnobl // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 28 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We construct an additional independent integral of motion for a class of three-dimensional minimally superintegrable systems with a constant magnetic field. This class was introduced in [J. Phys. A: Math. Theor. 50 (2017), 245202, 24 pages] and it is known to possess periodic closed orbits. In the present paper, we demonstrate that it is maximally superintegrable. Depending on the values of the parameters of the system, the newly found integral can be of arbitrarily high polynomial order in momenta.
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| ISSN: | 1815-0659 |