Examples of substitution systems and their factors

Abstract

The theory of substitution sequences and their higher-dimensional analogues is intimately connected with symbolic dynamics. By systematically studying the factors (in the sense of dynamical systems theory) of a substitution dynamical system, one can reach a better understanding of spectral and topological properties. We illustrate this point of view by means of some characteristic examples, including a rather universal substitution in one dimension as well as the squiral and the table tilings of the plane.

16 pages, 5 figures; minor updates

References in corpus (2)

• Pure Point Dynamical and Diffraction Spectra
• Dynamical versus diffraction spectrum for structures with finite local complexity

Cited by in corpus (6)

• Dynamical versus diffraction spectrum for structures with finite local complexity
• Aperiodic crystals and beyond
• Squirals and beyond: Substitution tilings with singular continuous spectrum
• Hexagonal inflation tilings and planar monotiles
• Spectral Theory of Substitutions in ${\mathbb{Z}}^d$
• Computations for symbolic substitutions