  In this note we complete the analysis carried on in [CGSV] about the
topological synchronisation of unimodal maps of the interval coupled in a
master-slave configuration, by answering to the questions raised in that paper.
Namely, we compute the weak limits of the invariant measure of the coupled
system as the coupling strength $k \in (0,1)$ tends to $0$ and to $1$ and
discuss the uniqueness of the invariant measure of its random dynamical system
counterpart.
  [CGSV] Caby Th., Gianfelice M., Saussol B., Vaienti S. "Topological
synchronisation or a simple attractor?" Nonlinearity Vol. 36, no. 7, pp.
3603-3621 (2023).
