An equivariant, inclination-flip, heteroclinic bifurcation

Abstract

We examine a heteroclinic bifurcation occurring in families of equivariant vector fields. Within these families, the flows contain structurally stable heteroclinic cycles. The flow can twist around the cycle to produce what is the equivalent of an `inclination-flip' homoclinic orbit. An unfolding of this bifurcation in a generic one-parameter equivariant family shows that Smale horseshoes are embedded in the flow for an open set of parameter values.