© 2015

Mathematics of Aperiodic Order

  • Johannes Kellendonk
  • Daniel Lenz
  • Jean Savinien

Part of the Progress in Mathematics book series (PM, volume 309)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Michael Baake, Matthias Birkner, Uwe Grimm
    Pages 1-32
  3. S. Akiyama, M. Barge, V. Berthé, J.-Y. Lee, A. Siegel
    Pages 33-72
  4. Lorenzo Sadun
    Pages 73-104
  5. Jean-Baptiste Aujogue, Marcy Barge, Johannes Kellendonk, Daniel Lenz
    Pages 137-194
  6. José Aliste-Prieto, Daniel Coronel, María Isabel Cortez, Fabien Durand, Samuel Petite
    Pages 195-222
  7. Natalie Priebe Frank
    Pages 223-257
  8. Antoine Julien, Johannes Kellendonk, Jean Savinien
    Pages 259-306
  9. David Damanik, Mark Embree, Anton Gorodetski
    Pages 307-370
  10. Svetlana Puzynina, Luca Q. Zamboni
    Pages 371-403
  11. Jean V. Bellissard
    Pages 405-428

About this book


What is order that is not based on simple repetition, that is, periodicity? How must atoms be arranged in a material so that it diffracts like a quasicrystal? How can we describe aperiodically ordered systems mathematically?

Originally triggered by the – later Nobel prize-winning – discovery of quasicrystals, the investigation of aperiodic order has since become a well-established and rapidly evolving field of mathematical research with close ties to a surprising variety of branches of mathematics and physics.

This book offers an overview of the state of the art in the field of aperiodic order, presented in carefully selected authoritative surveys. It is intended for non-experts with a general background in mathematics, theoretical physics or computer science, and offers a highly accessible source of first-hand information for all those interested in this rich and exciting field. Topics covered include the mathematical theory of diffraction, the dynamical systems of tilings or Delone sets, their cohomology and non-commutative geometry, the Pisot substitution conjecture, aperiodic Schrödinger operators, and connections to arithmetic number theory.


Pisot substitution conjecture aperiodic systems dynamical systems of tilings mathematical diffraction topology of tiling spaces

Editors and affiliations

  • Johannes Kellendonk
    • 1
  • Daniel Lenz
    • 2
  • Jean Savinien
    • 3
  1. 1.Institut Camille JordanUniversité Claude Bernard Lyon 1Villeurbanne CedexFrance
  2. 2.Mathematisches InstitutFriedrich-Schiller-Universität JenaJenaGermany
  3. 3.Institut Elie Cartan de LorraineUniversité de LorraineMetz Cedex 1France

Bibliographic information