  A few recent papers introduced the concept of topological synchronisation. We
refer in particular to \cite{TS}, where the theory was illustrated by means of
a skew product system, coupling two logistic maps. In this case, we show that
the topological synchronisation could be easily explained as the birth of an
attractor for increasing values of the coupling strength and the mutual
convergence of two marginal empirical measures. Numerical computations based on
a careful analysis of the Lyapunov exponents suggest that the attractor
supports an absolutely continuous physical measure (acpm). We finally show that
for some unimodal maps such acpm exhibit a multifractal structure.

Dynamical Systems