Computation of normal forms of differential equations associated with non-semisimple zero eigenvalues

This paper presents a method to compute the normal forms of differential eq uations whose Jacobian evaluated at an equilibrium includes a double zero o r a triple zero eigenvalue. The method combines normal form theory with cen ter manifold theory to deal with a general n-dimensional system. Explicit f ormulas are derived and symbolic computer programs have been developed usin g a symbolic computation language Maple. This enables one to easily compute normal forms and nonlinear transformations up to any order for a given spe cific problem. The programs can be conveniently executed on a main frame, a workstation or a PC machine without any interaction. Mathematical and prac tical examples are presented to show the applicability of the method.