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

Symmetry Integrability and Geometry-Methods and Applications

article

Antonella Marchesiello¹  Libor Šnobl² 

[1] Czech Technical University in Prague, Faculty of Information Technology, Department of Applied Mathematics;Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Department of Physics

关键词: integrability;    superintegrability;    higher order integrals;    magnetic field;   

DOI  :  10.3842/SIGMA.2018.092

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown