CALCULATING NORMAL FORMS FOR NONSEMI SIMPLE BIFURCATIONS

This paper presents a new scheme of calculating the Normal forms of a set of nonlinear ordinary differential equations when a nonsemi simple bifurcation occurs, with only the eigenvalues of zero real parts of the linearized differential equations given. It is well known that the classical matrix method enables one to establish the algebraic equations that govern the coefficients in the Normal form of a set of ordinary differential equations. However, it offers neither general technique of reducing the max...