Normal Forms and Computation for Four-dimension of General Nonlinear Dynamical Systems

For the traditional method to computer normal form, it is hard to carry out for programming and reply to reduce normal forms for high dimension.The authors study the normal forms for general cases of the four-dimensional nonlinear dynamical systems.For Jordan forms of the linear parts with two double zero and a pair of pure imaginary eigenvalues, with the aid of Maple program and adjoint operator, the authors propose the computation formula and coefficients relations with original system for seven order normal form with four-dimensional general nonlinear dynamical systems without reducing dimension for the first time.The introducing improved adjiont operator method which is convenient to program can effectually solve high dimension problem.