  The dynamics of globally coupled map lattices can be described in terms of a
nonlinear Frobenius--Perron equation in the limit of large system size. This
approach allows for an analytical computation of stationary states and their
stability. The complete bifurcation behaviour of coupled tent maps near the
chaotic band merging point is presented. Furthermore the time independent
states of coupled logistic equations are analyzed. The bifurcation diagram of
the uncoupled map carries over to the map lattice. The analytical results are
supplemented with numerical simulations.
