  This paper aims to review the measure synchronization, a weak form of
synchronization observed in coupled Hamiltonian systems, briefly. This
synchronization is characterized by a Hamiltonian system that displays either
quasiperiodic or chaotic dynamics. Each system, in the presence of either
linear or nonlinear coupling, shares a phase space domain with an identical
invariant measure in the measure synchronized state. It is important to note
that while the trajectories are identical in measure, they do not necessarily
exhibit complete temporal synchrony. This synchronization has been observed in
various physical systems, such as coupled pendulums, Josephson junctions, and
lasers.
