On reduced variational equations of coupled systems

A coupled system of three nonlinear oscillators with symmetric couplings is studied. It turns out that there exists a reduced variational equation to the in-phase periodic solution of such a coupled system. By the symmetry one establishes a structural property for the monodromy matrix of the reduced variational equation, which simplifies the computation of multipliers to a great extent. As an application of the above results, a coupled system of three Poincaré oscillators is discussed as well. Supported by the National Natural Science Foundation of China Zeng Xianwu: born in Dec. 1938, Professor