Abundance of attracting, repelling and elliptic periodic orbits in   two-dimensional reversible maps
  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. 
A. Delshams, S. V. Gonchenko, V. S. Gonchenko, J. T. L\'azaro and O.   Sten'kin
math.DS