The aim of this work is to present a comprehensive and up-to-date review of the main
physical properties (such as energy profiles, localization, scale laws, multifractal analysis …

To a given tiling a noncommutative space and the corresponding C*-algebra are
constructed. This includes the definition of a topology on the groupoid induced by …

In this work we consider the role of aperiodic order in different domains of science and
technology from an interdisciplinary approach. To start with, we introduce some general …

In this survey we discuss spectral and quantum dynamical properties of discrete one-
dimensional Schrödinger operators whose potentials are obtained by real-valued sampling …

Gap Labelling Theorems for Schrodinger Operators Page 1 Chapter 12 Gap Labelling
Theorems for Schrodinger Operators by Jean Bellissard Table of Contents 1. Introduction 1.1 …

We give new examples of discrete Schrödinger operators with potentials taking finitely many
values that have purely singular continuous spectrum. If the hull X of the potential is strictly …

We report on a new class of critical states in the energy spectrum of general Fibonacci
systems. By introducing a transfer matrix renormalization technique, we prove that the …

This book provides an interdisciplinary guide to quasicrystals, the 2011 Nobel Prize in
Chemistry winning topic, by presenting an up-to-date and detailed introduction to the many …

We investigate one-dimensional discrete Schrödinger operators whose potentials are
invariant under a substitution rule. The spectral properties of these operators can be …

The local structure of a tiling is described in terms of a multiplicative structure on its pattern
classes. The groupoid associated to the tiling is derived from this structure and its integer …