  We treat synchronization for iterated function systems generated by
diffeomorphisms on compact manifolds. Synchronization here means the
convergence of orbits starting at different initial conditions when iterated by
the same sequence of diffeomorphisms. The iterated function systems admit a
description as skew product systems of diffeomorphisms on compact manifolds
driven by shift operators. Under open conditions including transitivity and
negative fiber Lyapunov exponents, we prove the existence of a unique
attracting invariant graph for the skew product system. This explains the
occurrence of synchronization. The result extends previous results for iterated
function systems by diffeomorphisms on the circle, to arbitrary compact
manifolds.
