Singularidades de Equações Diferenciais Implícitas

Abstract

In this work we study implicit differential equations. Following the Thom tranversality theorem and the singularity theory we find an open and dense subset of this equation class that present only good singularity. This singularity are of six kind well folded saddle, well folded node, well folded focus, elliptical gather, hyperbolic gather. Davydov,in [8] showed the normal forms of a IDE in the case of well folded saddle, well folded node, well folded focus. In the case of gathered singularities, Davydov showed that the normal forms of IDE contains functional moduli. For a special class of implicit differential equation, the binary differential equation (BDE), we study the normal forms in the case in that the discriminant is a Morse function.