Multiplicidade de Equações Diferenciais Parciais de Primeira Ordem

Abstract

In this work we study the first order partial differential equations on the neighborhood of an isolated zero. Using the classification of singular points put by Izumiya in [27] and [28], we study the multiplicity of such equations introduced in [15]. When the first order partial differential equation defines an implicit differential equation, the definition of multiplicity coincides with the notion of multiplicity introduced by Bruce and Tari in [21]. We will also study the invariance of this multiplicity by smooth equivalence.