Title

Combinatorial and Topological Properties of a Family of Random Substitutions

Date of Award

2020

Document Type

Thesis

Degree Name

Master of Science in Mathematics

Department

Mathematics

First Advisor

Chrizaldy Neil C, Mañibo, Dr.math.; Eden Delight P. Miro, PhD

Abstract

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.

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