Speaker: Ibai Aedo (The Open University)
Abstract: We introduce substitutions of alphabets and explore their behaviour under iteration. This theory is enriched by considering collections of substitutions that generate semigroups of substitutions. Associated to each semigroup is a geometric object called a forward limit set, comprising a collection of infinite words in the alphabet. We will discuss properties of forward limit sets such as their size and their relationship to limit points of certain sequences in substitution dynamics known as S-adic sequences.