Dynamical 'strangeness' at the edge of chaos

A recently introduced class of dynamical systems, the generalized shifts, 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 border between order and chaos. Its anomalous dynamical properties are the result of a strong nonhyperbolicity which,in turn, is a manifestation of uncomputability in generalized shifts.