  We introduce a new method for determining the global stability of
synchronization in systems of coupled identical maps. The method is based on
the study of invariant measures. Besides the simplest non-trivial example,
namely two symmetrically coupled tent maps, we also treat the case of two
asymmetrically coupled tent maps as well as a globally coupled network. Our
main result is the identification of the precise value of the coupling
parameter where the synchronizing and desynchronizing transitions take place.
