Homoclinic tangencies leading to robust heterodimensional cycles

We consider \(C^r\) (\(r\geqslant 1\)) diffeomorphisms f defined on manifolds of dimension \(\geqslant 3\) with homoclinic tangencies associated to saddles. Under generic properties, we show that if the saddle is homoclinically related a blender then diffeomorphism can be approximated by \(C^1\) robust heterodimensional cycles. As an application, classic Simon–Asaoka’s examples also display In second hyperbolic sets. When entropy these sets large enough obtain cycles after perturbations.