3.4. Galois ambiguities for non-linear dynamical systems? Actually, the early prospects of differential Galois theory, especially in Drach’s plans, were much more ambitious. But in spite of the successes of differential algebra (Ritt, ...), it soon appeared that the foundations of differential Galois theory were not solid enough outside of the linear case. After various attempts by J.F. Pommaret (using Lie pseudo-groups) and H. Umemura (using infinite-dimensional formal groups), a new theory built by B. Malgrange seems extremely promising [23]. In the beginning, Malgrange9 remarked that another way to “save” Schlesinger’s theorem
