Synchronization in minimal iterated function systems on compact manifolds

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.Comment: 17 pages, to appear in Bulletin of the Brazilian Mathematical Society, New Serie

On the computation of hyperbolic sets and their invariant manifolds.

We describe a method for finding periodic orbits contained in a hyperbolic invariant set and of constructing their local stable and unstable manifolds, suitable to implement in a computer