Heterodimensional tangencies

We consider C-1-diffeomorphisms f defined on three-dimensional manifolds having a pair of saddles P-f and Q(f) (of unstable indices one and two) whose homoclinic classes coincide persistently. We prove that if the two-dimensional stable manifold of P-f and the two-dimensional unstable manifold of Q(f) have some non-transverse intersection (a heterodimensional tangency) the unfolding of such a tangency leads to diffeomorphisms h such that the homoclinic class of Q(h) (the continuation of Q(f) for h) is robustly non-dominated. This leads to the phenomena of (C-1-locally generic) coexistence of infinitely many sinks or sources and, in some relevant cases, to the coexistence of infinitely many minimal Cantor sets. We give examples where the previous dynamical configuration occurs, providing a natural transition from partially hyperbolic to robustly non-dominated dynamics.