The simplest erasing substitution

TL;DR

This paper introduces a new class of dynamical systems based on erasing substitution rules, analyzing a simple yet rich example that reveals complex properties and poses new research challenges.

Contribution

It is the first detailed study of dynamical systems generated by erasing substitution rules, focusing on a particularly simple yet intriguing example.

Findings

Analysis of geometric and analytical properties

Identification of complex dynamical behaviors

Presentation of new open problems

Abstract

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.