A System of $n=3$ Coupled Oscillators with Magnetic Terms: Symmetries and Integrals of Motion

The properties of a system of $n=3$ coupled oscillators with linear terms in the velocities (magnetic terms) depending in two parameters are studied. We proved the existence of a bi-Hamiltonian structure arising from a non-symplectic symmetry, as well the existence of master symmetries and additional integrals of motion (weak superintegrability) for certain particular values of the parameters.