Introduction

Abstract

A nonlinear equation should not be considered as the perturbation of a linear equation. We illustrate using two simple examples the importance of taking account of the singularity structure in the complex plane to determine the general solution of nonlinear equations. We then present the point of view of the Painlevé school to define new functions from nonlinear ordinary differential equations possessing a general solution which can be made single valued in its domain of definition (the Painlevé property).