Persistence of cycles and nonhyperbolic dynamics at heteroclinic bifurcations

Abstract

We construct an open set A of arcs of diffeomorphisms bifurcating through the creation of heterodimensional cycles (i.e. there are points in the cycle having different indices) being robustly nonhyperbolic after the unfolding of the cycle: every diffeomorphism is not hyperbolic. We also prove that the arcs in A exhibit cycles persistently. Finally, for generic arcs in A and for a full (Lebesgue) set of parameters values we prove that the resulting nonwandering set is transitive and local maximal.