On the geometry of master–slave synchronization

In 1990, Pecora and Carroll reported the observation that one can synchronize the orbits of two identical dynamical systems, which may be chaotic, by feeding state variables of one of them to the other one with no feedback, a phenomenon often called master–slave synchronization. We report here some results on the theory of master–slave synchronization for maps and flows, which are all inspired by a similar geometric and coordinate independent point of view to the one introduced in master–slave synchronization by Tresser, Worfolk, and Bass. Our results are variations on the theme that projection often can compensate for expansion.