Methode de centrage-estimation de l'erreur et comportement des trajectoires dans l'espace des phases

We establish certain estimates of the error of the averaging method for differential equations in Banach spaces in the 0, ∞ interval of the variable t. If there is an equilibrium point common to the exact and averaged equations, we study, under certain stability hypotheses, the behavior of the solutions of the exact equation according to the type of the equilibrium point for the averaged equation (node, focus, …).