Non-trivial wandering domains for heterodimensional cycles

We present a sufficient condition for three-dimensional diffeomorphisms having heterodimensional cycles to be approximated arbitrarily well by diffeomorphisms with non-trivial contracting wandering domains via several perturbations. The key idea is to show that diffeomorphisms with heterodimensional cycles associated with saddle points with non-real eigenvalues can be approximated by diffeomorphisms with generalized homoclinic tangencies presented by Tatjer. The generalized homoclinic tangency is an organizing center including a Bogdanov–Takens bifurcation, by which one can obtain non-trivial contracting wandering domains together with a Denjoy-like construction.