On dynamics and bifurcations of area-preserving maps with homoclinic   tangencies
  We study bifurcations of area-preserving maps, both orientable (symplectic) and non-orientable, with quadratic homoclinic tangencies. We consider one and two parameter general unfoldings and establish results related to the appearance of elliptic periodic orbits. In particular, we find conditions for such maps to have infinitely many generic (KAM-stable) elliptic periodic orbits of all successive periods starting at some number. 
Amadeu Delshams, Marina Gonchenko and Sergey Gonchenko
math.DS