Homoclinic tangencies leading to robust heterodimensional cycles
Abstract
We consider Cr (r≥slant 1) diffeomorphisms f defined on manifolds of dimension ≥slant 3 with homoclinic tangencies associated to saddles. Under generic properties, we show that if the saddle is homoclinically related to a blender then the diffeomorphism f can be Cr approximated by diffeomorphisms with C1 robust heterodimensional cycles. As an application, we show that the classic Simon-Asaoka's examples of diffeomorphisms with C1 robust homoclinic tangencies also display C1 robust heterodimensional cycles. In a second application, we consider homoclinic tangencies associated to hyperbolic sets. When the entropy of these sets is large enough we obtain C1 robust cycles after C1 perturbations.
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