Genericity conditions for finite cyclicity of elementary graphics

In this paper we explore the Khovanskii method for proving the finite cycli city of elementary graphics and how it can be applied in practice. The gene ricity conditions needed in that case form a proper subset of the usual met hods. Moreover some of the conditions are non-intrinsic and can be artifici ally created by action of the automorphism the automorphism groups preservi ng the normal forms near the singularities and their action on regular tran sitions. Hence we introduce an extension of the method which treats the usu al functional-Pfaffian systems together with the;the admissible changes of coordinates in the functional equations. (C) 1999 Academic Press.