Reduction de systemes differentiels perturbes

One considers a perturbed ordinary differential system which is then reduced to the non-perturbed corresponding system; i.e. the existence of a global relation between the solutions of the two systems is established. From this it is easy to deduce the difference between two correspondent solutions, and the theorems of existence for particular solutions (periodic, quasiperiodic,…) or integral manifolds, of the initial system.