An isolated saddle-node bifurcation occurring inside a horseshoe

In this paper, we consider a smooth arc of diffeomorphisms which has a saddle-node bifurcation ' inside ' a non-trivial invariant set which is a deformation of a horseshoe. We show that this saddle-node bifurcation is ' isolated ', that is, hyperbolicity is maintained before and after the saddle-node bifurcation. Moreover, we construct a C 2 -open set of arcs having the same property.