Combinatorial and Topological Properties of a Family of Random Substitutions

• Main Author: Escolano, Giovanni
• Format: text
• Published: Archīum Ateneo 2020
• Subjects: Pisot substitution, random substitution, semi-mixing, topological mixing.
• Online Access: https://archium.ateneo.edu/theses-dissertations/530
• Institution: Ateneo De Manila University

The combinatorial and topological properties of a large family of random substi- tutions, called the noble Pisa random substitutions, are studied. It is shown that each member of this family is a primitive irreducible Pisot random substitution. Using a specialised construction, a sufficient condition is established on the param- eters of the noble Pisa random substitutions to ensure that a compliant random sub- stitution admits recognisable words at all levels. It is proven that noble Pisa random substitutions, specified by parameters {n, p} ⊂ N \ {1}, induce symbolic dynamical systems that are not topologically mixing. Lastly, it is shown that the symbolic dynamical systems induced by the members of this family exhibit a weaker topological mixing property, called semi-mixing property.