GROUPS AND NONLINEAR DYNAMICAL-SYSTEMS DYNAMICS ON THE SU(2) GROUP

An abstract Newton-like equation on a general Lie algebra is introduce d such that orbits of the Lie-group action are attracting set. This eq uation generates the nonlinear dynamical system satisfied by the group parameters having an attractor coinciding with the orbit. The periodi c solutions of the abstract equation on a Lie algebra are discussed. T he particular case of the SU(2) group is investigated. The resulting n onlinear second-order dynamical system in R(3) as well as its constrai ned version referring to the generalized spherical pendulum are shown to exhibit global Hopf bifurcation.