Iterated function systems, skew product dynamics, partially hyperbolic dynamics

I'll consider iterated function systems generated by finitely many diffeomorphisms on compact manifolds. I'll discuss aspects of their dynamics, in particular minimality and synchronization.

These iterated function systems play a pivotal role in the study of dynamical systems: they correspond to dynamical systems of skew product type and provide examples of "partially hyperbolic dynamical systems". I'll discuss how iterated function systems are giving new results and insights in the study of partially hyperbolic dynamics.