The recognition of a class of bifurcation problems

In bifurcation theory there are two recognition problems concerning a given normal form, the recognition for the normal form and the recognition for universal unfoldings of bifurcation problems which are equivalent to the normal form. The two recognition problems for the normal forms εx2 + δλk were only partially solved. In this paper we give a complete solution of the two problems for all k 1 uniformly.  2003 Elsevier Science (USA). All rights reserved