Non-Fuchsian extension to the Painlevé test

Abstract

We consider meromorphic particular solutions of nonlinear ordinary differential equations and perform a perturbation à la Poincaré making their linearized equation non-Fuchsian at the movable pole and Fuchsian at infinity. When the nonlinear equation possesses movable logarithms, they are detected sooner than with the perturbative (Fuchsian) Painlevé test.