Lyapunov exponents for binary substitutions of constant length

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.

arXiv comment12 pages

References in corpus (6)

• Pure Point Dynamical and Diffraction Spectra
• Geometric properties of a binary non-Pisot inflation and absence of absolutely continuous diffraction
• Dynamical versus diffraction spectrum for structures with finite local complexity
• Spectrum of a Rudin-Shapiro-like sequence
• Scaling of the Thue-Morse diffraction measure
• Substitution-based sequences with absolutely continuous diffraction

Cited by in corpus (4)

• Spectral analysis of a family of binary inflation rules
• Inflation versus projection sets in aperiodic systems: The role of the window in averaging and diffraction
• Uniformly distributed orbits in ${\mathbb{T}}^d$ and singular substitution dynamical systems
• Absence of absolutely continuous diffraction spectrum for certain S-adic tilings