2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170414We apply topological methods to the study of the set of harmonic solutions of periodically perturbed autonomous ordinary differential equations on differentiable manifolds, allowing the perturbing term to contain a fixed delay. In the crucial step, in order to cope with the delay, we define a suitable (infinite dimensional) notion of Poincaré $T$-translation operator and prove a formula that, in the unperturbed case, allows the computation of its fixed point index.14 pagesDynamical SystemsClassical Analysis and ODEs34K13 (Primary) 34C25, 34K18 (Secondary)text