Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 092, 11 pages      arXiv:1804.03039      https://doi.org/10.3842/SIGMA.2018.092

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

Antonella Marchesiello a and Libor Šnobl b
a) Czech Technical University in Prague, Faculty of Information Technology, Department of Applied Mathematics, Th\'akurova 9, 160 00 Prague 6, Czech Republic
b) Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Department of Physics, B\v rehová 7, 115 19 Prague 1, Czech Republic

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

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.

Key words: integrability; superintegrability; higher order integrals; magnetic field.

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