Non-critical saddle-node cycles and robust non-hyperbolic dynamics

We study arcs of diffeomorphisms (f(t)) in manifolds of dimension greater than or equal to three bifurcating via non-critical saddle-node cycles. We construct an open set S of such arcs for which, after the bifurcation, every diffeomorphism f(t) does not satisfy Axiom A. We also exhibit an open subset S' of S such that after the bifurcation every diffeomorphism has a partially hyperbolic set of saddle-type which is persistent, locally maximal and transitive. As a consequence, we get a submanifold of codimension-1 of diffeomorphisms with a saddle-node that locally separates the set of Morse-Smale systems from the diffeomorphisms with a partially hyperbolic transitive set.