Existence and structure of complete formal solutions of non-linear meromorphic systems of ordinary differential equations

Abstract

For general non-linear n-dimensional homogeneous systems of meromorphic ODE, we show existence of a complete formal solution, formally depending upon n free parameters. We investigate the structure of such formal solutions and, in particular, obtain a factorization, analogous to results of J.-P. Ramis and (independently) the author for linear systems.