Computation Of Simplest Normal Forms Of Differential Equations Associated With A Double-Zero Eigenvalue

. In this paper a method is presented for computing the simplest normal form of dierential equations associated with the singularity of a double zero eigenvalue. Based on a conventional normal form of the system, explicit formulae for both generic and non-generic cases are derived, which can be used to compute the coecients of the simplest normal form and the associated nonlinear transformation. The recursive algebraic formulae have been implemented on computer systems using Maple. The user-friendly programs can be executed without any interaction. Examples are given to demonstrate the computational eciency of the method and computer programs. The author to receive correspondence. Email: [email protected] Y. Yuan and P. Yu Computation of Simplest Normal Forms 2 1. Introduction Normal form theory is one of the useful tools in analyzing complex dynamical behaviour of a nonlinear system such as bifurcation and instability. The method, based on successive coordinate transforma..