  Globally coupled doubling maps are studied in this paper. In this setting and
for finitely many sites, two distinct bifurcation values of the coupling
strength have been identified in the literature, corresponding to the emergence
of contracting directions (\cite{koiller2010coupled}) and, specifically for
$N=3$ sites, to the loss of ergodicity (\cite{fernandez2014breaking}). On the
one hand, we reconsider these results and provide an interpretation of the
observed dynamical phenomena in terms of the synchronization of the sites. On
the other hand, we initiate a new point of view which focuses on the evolution
of distributions and allows to incorporate the investigation of infinitely many
sites. In particular we observe phenomena in the infinite system that is
analogous to the limit states of the contracting regime of $N=3$ sites.
