Abstract. We study dynamics and bifurcations of two-dimensional reversible
maps having non-transversal heteroclinic cycles containing symmetric saddle
periodic points. We consider one-parameter families of reversible maps unfolding
generally the initial heteroclinic tangency and prove that there are infinitely
sequences (cascades) of bifurcations of birth of asymptotically stable and unstable
as well as elliptic periodic orbits.
Delshams, A. [et al.]. "Abundance of attracting, repelling and elliptic periodic orbits in two-dimensional reversible maps". 2012.