Random substitutions are a natural generalisation of their classical 'deterministic'counterpart
, whereby at every step of iterating the substitution, instead of replacing a letter with a …

Due to the absence of periodic length scale, electronic states and their topological
properties in quasicrystals have been barely understood. Here, we focus on one …

Orbit separation dimension (OSD), previously introduced as amorphic complexity, is a
powerful complexity measure for topological dynamical systems with pure-point spectrum …

This chapter is about the tiling dynamical systems approach to the study of aperiodic order.
We compare and contrast four related types of systems: ordinary (one-dimensional) …

In this paper, we investigate the structure of the most general kind of substitution shifts,
including non-minimal ones, and allowing erasing morphisms. We prove the decidability of …

A central motive of this thesis is the study of configurations with aperiodic order. Here, a
configuration may refer to a bi-infinite sequence of symbols, a tiling of the plane or a …

In this paper, we deal with reversing and extended symmetries of subshifts generated by
bijective substitutions. We survey some general algebraic and dynamical properties of these …

In this contribution, we discuss the automorphism group, ie, the centralizer of the shift action
inside the group of self-homeomorphisms of a subshift, together with the extended symmetry …

We study substitutive systems generated by nonprimitive substitutions and show that
transitive subsystems of substitutive systems are substitutive. As an application we obtain a …

This thesis deals with dynamical and arithmetic properties of substitutive sequences. A
major theme explored here is the belief that object coming from substitutions of indepen dent …