  Two-dimensional mappings obtained by coupling two piecewise increasing
expanding maps are considered. Their dynamics is described when the coupling
parameter increases in the expanding domain. By introducing a coding and by
analysing an admissibility condition, approximations of the corresponding
symbolic systems are obtained. These approximations imply that the topological
entropy is located between two decreasing step functions of the coupling
parameter. The analysis firstly applies to mappings with piecewise affine local
maps which allow explicit expressions and, in a second step, is extended by
continuity to mappings with piecewise smooth local maps.
