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 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209865 |
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| 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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Marchesiello, A. Šnobl, L. 2025-11-27T18:03:32Z 2018 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. 1815-0659 2010 Mathematics Subject Classification: 37J35; 78A25 arXiv: 1804.03039 https://nasplib.isofts.kiev.ua/handle/123456789/209865 https://doi.org/10.3842/SIGMA.2018.092 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. This research was supported by the Grant Agency of the Czech Republic, project 17-11805S. The authors thank Pavel Winternitz for discussions on the subject of this paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications An Infinite Family of Maximally Superintegrable Systems in a Magnetic Field with Higher Order Integrals Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
An Infinite Family of Maximally Superintegrable Systems in a Magnetic Field with Higher Order Integrals |
| spellingShingle |
An Infinite Family of Maximally Superintegrable Systems in a Magnetic Field with Higher Order Integrals Marchesiello, A. Šnobl, L. |
| title_short |
An Infinite Family of Maximally Superintegrable Systems in a Magnetic Field with Higher Order Integrals |
| title_full |
An Infinite Family of Maximally Superintegrable Systems in a Magnetic Field with Higher Order Integrals |
| title_fullStr |
An Infinite Family of Maximally Superintegrable Systems in a Magnetic Field with Higher Order Integrals |
| title_full_unstemmed |
An Infinite Family of Maximally Superintegrable Systems in a Magnetic Field with Higher Order Integrals |
| title_sort |
infinite family of maximally superintegrable systems in a magnetic field with higher order integrals |
| author |
Marchesiello, A. Šnobl, L. |
| author_facet |
Marchesiello, A. Šnobl, L. |
| publishDate |
2018 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/209865 |
| citation_txt |
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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| first_indexed |
2025-12-07T19:30:44Z |
| last_indexed |
2025-12-07T19:30:44Z |
| _version_ |
1850886172468838400 |