Analytic continuation of the solution of a nonlinear holomorphic differential system (Q2712944)

From the introduction (translation from the French): We adapt to a nonlinear holomorphic differential system the analytic continuation methods applied in [\textit{Y. Hamada}, \textit{J. Leray} and \textit{A. Takeuchi}, J. Math. Pures Appl. (9) 64, 257-319 (1985; Zbl 0581.32017)] to a linear holomorphic partial differential equation. When this equation is of first-order, one derives its solution from that of its characteristic system, which is nonlinear. The following question thus arose: Can the techniques of [op. cit.] be adapted to a nonlinear holomorphic differential system?NEWLINENEWLINENEWLINEThis we achieve in the present article. We rely on various sections [op. cit.], which are not merely cited but often reproduced for the sake of intelligibility. This article is simpler than the previous one and can thus be read in preparation for reading the latter.NEWLINENEWLINEFor the entire collection see [Zbl 0957.00059].