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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2018
Hauptverfasser: Marchesiello, A., Šnobl, L.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2018
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/209865
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren: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.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
_version_ 1862732249799065600
author Marchesiello, A.
Šnobl, L.
author_facet Marchesiello, A.
Šnobl, L.
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.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
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.
first_indexed 2025-12-07T19:30:44Z
format Article
fulltext
id nasplib_isofts_kiev_ua-123456789-209865
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-07T19:30:44Z
publishDate 2018
publisher Інститут математики НАН України
record_format dspace
spelling 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
spellingShingle An Infinite Family of Maximally Superintegrable Systems in a Magnetic Field with Higher Order Integrals
Marchesiello, A.
Šnobl, L.
title 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_short 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
url https://nasplib.isofts.kiev.ua/handle/123456789/209865
work_keys_str_mv AT marchesielloa aninfinitefamilyofmaximallysuperintegrablesystemsinamagneticfieldwithhigherorderintegrals
AT snobll aninfinitefamilyofmaximallysuperintegrablesystemsinamagneticfieldwithhigherorderintegrals
AT marchesielloa infinitefamilyofmaximallysuperintegrablesystemsinamagneticfieldwithhigherorderintegrals
AT snobll infinitefamilyofmaximallysuperintegrablesystemsinamagneticfieldwithhigherorderintegrals