Normal forms for certain singularities of smooth map-germs (Q1819426)

In the theory of singularities of smooth mappings, the classification of map germs is very important. But, it is very difficult except for the case of smooth functions. The author proves a normal form theorem for formal mappings which is an analog of Takens' normal form theorem for vector fields. As a corollary of the normal form theorem, he states a generalized splitting theorem. He also gives a classification of smooth map germs f: (\({\mathbb{R}}^ n,0)\to ({\mathbb{R}}^ 2,0)\) as an application of the generalized splitting theorem.