We present a skew system made of two unimodal maps of the interval coupled in a master-slave configuration. This system arises in the physics literature as an explanatory model of the so-called topological synchronization, i.e. the mechanism believed to be at the basis of emerging collective phenomena in coupled chaotic systems.
We discuss the synchronization phenomenon looking at the weak limit of
the empirical measure of the slave system and to the multifractal spectrum
of the driving map in the strong coupling regime.
Moreover, in order to understand the evolution of the original skew
system, we study a family of random dynamical systems, closer to this
in its definition, indexed by the original coupling parameter and discuss
the existence of the invariant measures for such systems especially in the
strong and weak coupling limits.
Joint work with Th. Caby, B. Saussol and S. Vaienti.