2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62234Here we show that for a C^2 surface diffeomorphism that satisfy the hypothesis of Hayashi connecting lemma either can be approximated, in the C^1 topology, by a diffeomorphism exhibiting a homoclinic tangency or the diffeomorphism already presented transversal homoclinic orbits.Dynamical Systems37D45;70K44text