Substitutions in Dynamics, Arithmetics and Combinatorics

  • N. Pytheas Fogg
  • Valéré Berthé
  • Sébastien Ferenczi
  • Christian Mauduit
  • Anne Siegel

Part of the Lecture Notes in Mathematics book series (LNM, volume 1794)

Table of contents

About this book

Introduction

A certain category of infinite strings of letters on a finite alphabet is presented here, chosen among the 'simplest' possible one may build, both because they are very deterministic and because they are built by simple rules (a letter is replaced by a word, a sequence is produced by iteration). These substitutive sequences have a surprisingly rich structure.
The authors describe the concepts of quantity of natural interactions, with combinatorics on words, ergodic theory, linear algebra, spectral theory, geometry of tilings, theoretical computer science, diophantine approximation, trancendence, graph theory. This volume fulfils the need for a reference on the basic definitions and theorems, as well as for a state-of-the-art survey of the more difficult and unsolved problems.

Keywords

Alphabet Combinatorics Diophantine approximation Partition Symbolic dynamics automata automata sequences combinatorics on words dynamical systems ergodic theory fractal graph theory substitutive dynamical systems

Editors and affiliations

  • N. Pytheas Fogg
    • 1
  • Valéré Berthé
    • 2
  • Sébastien Ferenczi
    • 2
  • Christian Mauduit
    • 2
  • Anne Siegel
    • 3
  1. 1.MarseilleFrance
  2. 2.IML, Case 907Univ.de la MéditerraneéMarseille Cedex 09France
  3. 3.Campus de BeaulieuIRISARennes CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/b13861
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-44141-0
  • Online ISBN 978-3-540-45714-5
  • Series Print ISSN 0075-8434
  • About this book