Bifurcation from Codimension One Relative Homoclinic Cycles

We study bifurcations of relative homoclinic cycles in flows that are equivariant under the action of a finite group. The relative homoclinic cycles we consider are not robust, but have codimension one. We assume real leading eigenvalues and connecting trajectories that approach the equilibria along leading directions. We show how suspensions of subshifts of finite type generically appear in the unfolding. Descriptions of the suspended subshifts in terms of the geometry and symmetry of the connecting trajectories are provided.