Complexity and directional entropy in two dimensions

Ryan Broderick, Van Cyr, Bryna Kra

Published 2014-09-17Version 1

We study the directional entropy of the dynamical system associated to a $\Z^2$ configuration in a finite alphabet. We show that under local assumptions on the complexity, either every direction has zero topological entropy or some direction is periodic. In particular, we show that all nonexpansive directions in a $\Z^2$ system with the same local assumptions have zero directional entropy.