Groups and nonlinear dynamical systems: Chaotic dynamics on the SU(2) × SU(2) group

In our previous paper, Groups and nonlinear dynamical systems, dynamics on the SU(2) group, in Physica D, 1996, 99, 237, we introduced an abstract Newton-like equation on a general Lie algebra such that submanifolds fixed by the second-order Casimir operator are attracting sets. The corresponding group parameters satisfy the nonlinear dynamical system having an attractor coinciding with the submanifold. In this work, we discuss the case with the SU(2) × SU(2) group. The resulting second-order system in 6 is demonstrated to exhibit chaotic behaviour.