Antonella Marchesiello, Libor Šnobl, “An Infinite Family of Maximally Superintegrable Systems in a Magnetic Field with Higher Order Integrals”, SIGMA, 2018, Volume 14,092, 11 pp.

This article is cited in 13 papers

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

Antonella Marchesiello^a, Libor Šnobl^b

^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

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.

MSC: 37J35; 78A25

Received: April 10, 2018; in final form August 24, 2018; Published online August 31, 2018

Language: English

DOI: 10.3842/SIGMA.2018.092