  We prove that heterodimensional cycles can be created by unfolding a pair of
homoclinic tangencies in a certain class of C-infinity diffeomorphisms. This
implies the existence of a C2- open domain in the space of dynamical systems
with a certain type of symmetry where systems with heterodimensional cycles are
dense in C-infinity. In particular, we describe a class of three-dimensional
flows with a Lorenz-like attractor such that an arbitrarily small perturbation
of any such flow can belong to this domain - in this case the corresponding
heterodimensional cycles belong to a chain-transitive attractor of the
perturbed flow.
