Dynamical Systems Arising from Substitutions

Abstract

In this chapter, and in the two forthcoming chapters, we are dealing with particular sequences, generated by a substitution on a finite alphabet (substitutive and automatic sequences). There exist a lot of contributions around these sequences, many of which are concerned with their combinatorial and arithmetical properties, others with the properties of the associated topological system and more recently, geometric aspects have been intensively studied. J.P. Allouche and J. Shallit have devoted a substantial book to Automatic Sequences [14] while all recent results on substitutions have been gathered in an impressive collective work [88].