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Symmetry, Integrability and Geometry: Methods and Applications, 2018, Volume 14, 092, 11 pp.
DOI: https://doi.org/10.3842/SIGMA.2018.092 (Mi sigma1391) 		 
This article is cited in 13 scientific papers (total in 13 papers)

An Infinite Family of Maximally Superintegrable Systems in a Magnetic Field with Higher Order Integrals

Antonella Marchesielloa, Libor Šnoblb

a Czech Technical University in Prague, Faculty of Information Technology, Department of Applied Mathematics, Thákurova 9, 160 00 Prague 6, Czech Republic
b Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Department of Physics, Břehová 7, 115 19 Prague 1, Czech Republic
Full-text PDF (348 kB) Citations (13)
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DOI: https://doi.org/10.3842/SIGMA.2018.092
Abstract: We construct an additional independent integral of motion for a class of three dimensional minimally superintegrable systems with 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.
Keywords: integrability; superintegrability; higher order integrals; magnetic field.
Funding agency Grant number
Grantová Agentura České Republiky 17-11805S
This research was supported by the Grant Agency of the Czech Republic, project 17-11805S.
Received: April 10, 2018; in final form August 24, 2018; Published online August 31, 2018
Bibliographic databases:
Document Type: Article
MSC: 37J35; 78A25
Language: English
Citation: Antonella Marchesiello, Libor Šnobl, “An Infinite Family of Maximally Superintegrable Systems in a Magnetic Field with Higher Order Integrals”, SIGMA, 14 (2018), 092, 11 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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