  We study dynamics and bifurcations of 2-dimensional reversible maps having a
symmetric saddle fixed point with an asymmetric pair of nontransversal
homoclinic orbits (a symmetric nontransversal homoclinic figure-8). We consider
one-parameter families of reversible maps unfolding the initial homoclinic
tangency and prove the existence of infinitely many sequences (cascades) of
bifurcations related to the birth of asymptotically stable, unstable and
elliptic periodic orbits.
