A recently introduced class of dynamical systems, the generalized shif
ts, is shown to exhibit both topological chaos, while being metrically
ordered, and a phase transition in the framework of the thermodynamic
formalism when this is applied to its entropic properties. Therefore,
it provides a further example of complex behaviour emerging at the bo
rder between order and chaos. Its anomalous dynamical properties are t
he result of a strong nonhyperbolicity which,in turn, is a manifestati
on of uncomputability in generalized shifts.