Regimes of stability of accelerator modes
  The phase diagram of a simple area-preserving map, which was motivated by the quantum dynamics of cold atoms, is explored analytically and numerically. Periodic orbits of a given winding ratio are found to exist within wedge-shaped regions in the phase diagrams, which are analogous to the Arnol'd tongues which have been extensively studied for a variety of dynamical systems, mostly dissipative ones. A rich variety of bifurcations of various types are observed, as well as period doubling cascades. Stability of periodic orbits is analyzed in detail. 
Rebecca Hihinashvili, Tali Oliker, Yaniv S. Avizrats, Alexander Iomin,   Shmuel Fishman, Italo Guarneri