Solutions périodiques d'une équation de Riccati généralisée

Abstract

The intention of this memoir is to analyze the relationship between the dynamics of limit cycles in planar di¤erential systems ( _ x = P (x; y) _ y = Q (x; y)) and the analytical properties of generalized Riccati equations. It will attempt, using a qualitative and transformational approach, to analyze how some representations of the Riccati equation could predict or describe the existence of limit cycles in non-linear systems.