Entropy for symbolic dynamics with overlapping alphabets

Fabio Drucker, David Richeson, Jim Wiseman

Published 2010-11-15Version 1

We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces, give several techniques for computing lower bounds for it, and show that it is equal to a limit of entropies of (standard) full shifts. When a shift space with overlaps arises as a model for a discrete dynamical system with a finite set of overlapping neighborhoods, the entropy gives a lower bound for the topological entropy of the dynamical system.