Homomorphisms of symbolic dynamical systems

Abstract

The densities of finite blocks of symbols can be computed for points in any substitution minimal set arising from a substitution of constant length and also for points in any Sturmian minimal set. It follows from the computations that all Sturmian minimal sets and all substitution minimal sets are strictly ergodic and have topological entropy zero. It also follows that no Sturmian minimal set is the homomorphic image of a substitution minimal set. It can also be shown that no non-trivial substitution minimal set is powerfully (totally) minimal, and it follows that no non-trivial substitution minimal set is the homomorphic image of a Sturmian minimal set.