On the computation of the coefficients associated with high order normal forms

A new procedure for obtaining high order normal forms and the associated coefficients is presented. It is assumed that the Jacobian of the system considered is in a diagonal form. In comparison with existing normal form approaches, this procedure lends itself more readily to symbolic calculations, like MAPLE, and the calculations of high order normal forms, together with the associated coefficients, are carried out much more conveniently. To illustrate the approach, five examples are presented. Examples 1 and 3 also contain a comparison of the results obtained by the methods of normal forms and averaging. (C) 2000 Academic Press.