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

SIGMA 1 (2005), 004, 7 pages      nlin.SI/0511007      https://doi.org/10.3842/SIGMA.2005.004

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

Manuel F. Rañada
Departamento de Física Teórica, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain

Received July 06, 2005, in final form September 16, 2005; Published online September 20, 2005

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. 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.

Key words: non-symplectic symmetries; bi-Hamiltonian structures; master symmetries; cubic integrals.

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