Sobre a geometria dos conjuntos críticos de operadores diferenciais de primeira ordem

Abstract

Based on the paper Morin Singularities and Global Geometry in a Class of Ordinary Differential Operators, by I. Malta, N. Saldanha and C. Tomei, the aim of this work is to give a characterization of the critical set of the first order differential operator F(u) =u + f (u) with domain in the Banach space of periodic functions with continuous and periodic derivatives and taking value in the Banach space of continuous periodicfunctions, where f is a generic nonlinearity. We show that a global changes of variables in both domain and image transforms the operator into a simple normal form. In the special case f (u) = u2, we show that all critical points are folds.