2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77582In this paper, we consider a smooth arc of diffeomorphisms which has a saddle-node bifurcation inside a nontrivial invariant set which is a deformation of a horseshoe. We show that this saddle-node bifurcation is isolated, that is, its hyperbolicity is maintained before and after the saddle-node bifurcation. Moreover we construct a $C^2$-open set of arcs having the same property.18 pages, 4 figures, to apper Dynamics and Stability of SystemsDynamical Systems58F09; 58F14; 58F15text