Synchronization time in a hyperbolic dynamical system with long-range interactions

We show that the threshold of complete synchronization in a lattice of coupled non-smooth chaotic maps is determined by linear stability along the directions transversal to the synchronization subspace. We examine carefully the synchronization time and show that an inadequate observation of the system evolution leads to wrong results. We present both careful numerical experiments and a rigorous mathematical explanation confirming this fact, allowing for a generalization involving hyperbolic coupled map lattices.