  In our previous paper: K. Kowalski and J. Rembieli\'nski, Groups and
nonlinear dynamical systems. Dynamics on the SU(2) group, Physica D 99, 237
(1996), we introduced an abstract Newton-like equation on a general Lie algebra
such that submanifolds fixed by the second-order Casimir operator are
attracting set. 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 $SU(2)\times SU(2)$ group. The resulting
second-order system in $R^6$ is demonstrated to exhibit chaotic behaviour.
