# Lyapunov exponents for binary substitutions of constant length

## TL;DR

This paper introduces a Lyapunov exponent-based method to confirm the absence of absolutely continuous diffraction in binary substitutions of constant length, offering an alternative to Dekking's criterion.

## Contribution

It presents a new approach using Lyapunov exponents derived from Fourier matrices to analyze diffraction properties of binary substitutions.

## Key findings

- Positive Lyapunov exponents confirm absence of absolutely continuous diffraction
- Applicable to all primitive, aperiodic binary substitutions of constant length
- Provides an independent method from Dekking's criterion

## Abstract

A method of confirming the absence of absolutely continuous diffraction via the positivity of Lyapunov exponents derived from the corresponding Fourier matrices is presented, which provides an approach that is independent of previous results on the basis of Dekking's criterion. This yields a positive result for all constant length substitutions on a binary alphabet which are primitive and aperiodic.