ADJOINT OPERATOR METHOD AND NORMAL FORMS OF HIGHER ORDER FOR NONLINEAR DYNAMICAL SYSTEM

摘要

Normal form theory is, a very effective method when we study degeneratebifurcations of nonlinear dynamical systems. In this paper by using adjoint operatormethod, normal forms of order 3 and 4 for nonlinear dynamical system with nilpotentlinear part and Z2-asymmetry are computed. According to normal forms obtained,universal unfoldings for some degenerate bifurcation cases of codimension 3 and simpleglobal characterizations, are studied.