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Substitutions in Dynamics, Arithmetics and Combinatorics Book

Substitutions in Dynamics, Arithmetics and Combinatorics
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  • Substitutions in Dynamics, Arithmetics and Combinatorics
  • Written by author N. Pytheas Fogg
  • Published by Springer-Verlag New York, LLC, August 2009
  • 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 wo
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Authors

Preface
List of contributors
1Basic notions on substitutions1
Pt. IArithmetics and combinatorics of substitutions
2Substitutions, arithmetic and finite automata: an introduction35
3Automatic sequences and transcendence53
4Substitutions and partitions of the set of positive integers81
Pt. IIDynamics of substitutions
5Substitutions and symbolic dynamical systems101
6Sturmian Sequences143
7Spectral theory and geometric representation of substitutions199
8Diophantine approximations, substitutions, and fractals253
Pt. IIIExtensions to free groups and interval transformations
9Infinite words generated by invertible substitutions295
10Polynomial dynamical systems associated with substitutions321
11Piecewise linear transformations of the unit interval and Cantor sets343
12Some open problems363
AUndecomposable matrices in dimension 3375
References377
Index399


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