Dynamics of interval maps generated by erasing substitutions

Abstract

We study the discrete dynamics of interval maps generated by the action of erasing block substitutions on the binary expansion. We propose a classification of erasing block substitutions in a hierarchy of classes displaying progressively stronger erasing character. We investigate how this affects the dynamics of the corresponding interval maps, showing that the richest dynamical behavior (Devaney and Li-Yorke chaos, infinite topological entropy) is achieved at a precise step in this hierarchy, which we name completely erasing substitutions.