2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138854We consider an autonomous system in R^n having a limit cycle x_0 of period T>0 which is nondegenerate in a suitable sense. We then consider the perturbed system obtained by adding to the autonomous system a T-periodic, not necessarily differentiable, term whose amplitude tends to 0 as a small parameter e>0 tends to 0. Assuming the existence of a T-periodic solution x_e of the perturbed system and its convergence to x_0 as e->0, the paper establishes the existence of d_e->0 as e->0 such that \|x_e(t+d_e)-x_0(t)\|<=eM for some M>0 and any e>0 sufficiently small.To Appear in Commun. Pure Appl. AnalClassical Analysis and ODEs34A10, 34C24text