The simplest erasing substitution

In this work, we begin the study of a new class of dynamical systems determined by interval maps generated by the symbolic action of erasing substitution rules. We do this by discussing in some detail the geometric, analytical, dynamical and arithmetic properties of a particular example, which has the virtue of being arguably the simplest and that at the same time produces interesting properties and new challenging problems.

Automated summary

This work begins the study of a new class of dynamical systems determined by interval maps generated by the symbolic action of erasing substitution rules. It discusses in detail the geometric, analytical, dynamical, and arithmetic properties of a specific example, which is argued to be the simplest and yet produces interesting properties and new challenging problems.