# Symbolic dynamics

## Description

Symbolic dynamics generally studies properties of invariant sets and measures which are defined on infinite sequences of characters of a fixed (finite or countably infinite) alphabet.

One example of such a system arises from a *substitution*.
A (deterministic) substitution consists of a finite alphabet along with a set of transformation rules.
A classical example is the Fibonacci substitution, which is composed of the transformations taking `a` to `ab` and `b` to `a`.
Random substitutions are a generalization of deterministic substitutions where a transformation rule is chosen randomly from a list of rules.
Deterministic and random substitutions have associated dynamical systems and invariant measures, which capture certain “asymptotic statistics” of the substitution.

In my joint paper with Andrew Mitchell, we study the multifractal properties of measure associated with random substitutions.

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## Relevant Research Articles

- Multifractal analysis of measures arising from random substitutions
With: Andrew Mitchell Journal: *Comm. Math. Phys.***405**(2024), Paper No. 63, 44 p.Links: pdfdoizblarxiv