Automatic Classiication of Normal Forms

The aim of this paper is to demonstrate a speciic application of Computer Algebra to bifurcation theory with symmetry. The classiication of diierent bifurcation phenomena in case of several parameters is automated, based on a classiication of Grr obner bases of possible tangent spaces. The computations are performed in new coordinates of fundamental invariants and fundamental equivariants, with the induced weighted ordering. In order to justify the approach the theory of intrinsic modules is applied. Results for the groups D 3 ; Z 2 ; and Z 2 Z 2 demonstrate that the algorithm works independent of the group and that new results are obtained.