Abstract. 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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.