Synchronization of coupled uniform piecewise linear three-dimensional Markov maps

Three-dimensional uniform piecewise linear Markov maps with two linear regions per coordinate are considered. Two such maps are coupled via a state in a master-slave configuration. It is shown that, except for special values of the parameters, synchronization of the iterates of two coupled maps takes place. The time needed to reach synchronization depends on the initial conditions. Usually, it is rather short, but for certain initial conditions many iterations are needed