  Integration of nonlinear dynamical systems is usually seen as associated to a
symmetry reduction, e.g. via momentum map. In Lax integrable systems, as
pointed out by Kazhdan, Kostant and Sternberg in discussing the Calogero
system, one proceeds in the opposite way, enlarging the nonlinear system to a
system of greater dimension. We discuss how this approach is also fruitful in
studying non integrable systems, focusing on systems in normal form.
