  The problem of synchronization of coupled Hamiltonian systems exhibits
interesting features due to the non-uniform or mixed nature (regular and
chaotic) of the phase space. We study these features by investigating the
synchronization of unidirectionally coupled area-preserving maps coupled by the
Pecora-Carroll method. We find that coupled standard maps show complete
synchronization for values of the nonlinearity parameter at which regular
structures are still present in phase space. The distribution of
synchronization times has a power law tail indicating long synchronization
times for at least some of the synchronizing trajectories. With the
introduction of coherent structures using parameter perturbation in the system,
this distribution crosses over to exponential behavior, indicating shorter
synchronization times, and the number of initial conditions which synchronize
increases significantly, indicating an enhancement in the basin of
synchronization. On the other hand, coupled blinking vortex maps display both
phase synchronization and phase slips, depending on the location of the initial
conditions. We discuss the implication of our results.
