Symmetries and constants of motion of a system of three oscillators with magnetic terms

Abstract:
The properties of a system of $n=3$ coupled oscillators  with linear terms in the velocities (magnetic terms) depending in two parameters are studied.  It is proved the existence of a bi-Hamiltonian structure  arising from a non-symplectic symmetry, as well the existence of additionals integrals of motion for certain particular values of the parameters.