Binary Boundary Singularity Identification And Limited Conclusive

The classification of boundary singularities has been rediscovered several times by various authors(see, for example,[1 ,6,10,45]).For those singularities of two variables, they are very similar to the classification of bifurcation problems with one state variable. But this connection has apparently gone unnoticed. The study of this connection leads us naturally to solve recognition problems for bivariate boundary singularities.The other half of this paper is to consider a special case of Arnold's result on semiquasihomogeneous germ. Unlike his proof, we found a very elementary proof for this special case , and particularly, it completes the discussion of Cen's result[25, 60].