[For the entire collection see Zbl 0552.00005.]
The paper deals with the \({\mathcal A}\)-classification of smooth map germs. First the author obtains some normal form theorems which give an efficient and simply way of doing this classification (sometimes).
These results are analogies of F. Takens’ normal form theorem for vector fields [Publ. Math., Inst. Hautes Étud. Sci. 43(1973), 47-100 (1974; Zbl 0279.58009)] and of the method of complete transversals introduced for the \({\mathcal K}\)-classification of map germs by the reviewer and C. G. Gibson [Q. J. Math., Oxf. II. Ser. 34, 281-295 (1983; Zbl 0537.58007) and Math. Scand. (to appear)]. Using these normal form theorems, some splitting lemmas for corank 1 map-germs are proved. As an application, the \({\mathcal A}\)-classification of finitely determined map germs \((R^ n,0)\to (R^ 2,0)\) with corank 1 and nontrivial 3-jets is given.