Dynamics of interval maps generated by erasing substitutions

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.