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.
Substitutions in Dynamics, Arithmetics and Combinatorics
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Inside This Book
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First Sentence:
The aim of this chapter is to introduce some concepts and to fix the notation we will use throughout this book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
substitutive dynamical system, nontrivial coboundary, maximal equicontinuous factor, contracting plane, most linear complexity, toral translation, substitutive system, toral rotations, constant length substitutions, invertible substitutions, dyadic rotation, unimodular substitution, adic transformation, abelianization map, primitive substitution, nonconstant length, algebraic formal power series, symbolic dynamical systems, topological dynamical system, dyadic development, purely discrete spectrum, coincidence condition, conjugacy map, generalized substitutions, biinfinite sequences Key Phrases - Capitalized Phrases (CAPs): (learn more)
Mendès France, The Chacon, The Hadamard, Bounded Gaps New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The aim of this chapter is to introduce some concepts and to fix the notation we will use throughout this book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
substitutive dynamical system, nontrivial coboundary, maximal equicontinuous factor, contracting plane, most linear complexity, toral translation, substitutive system, toral rotations, constant length substitutions, invertible substitutions, dyadic rotation, unimodular substitution, adic transformation, abelianization map, primitive substitution, nonconstant length, algebraic formal power series, symbolic dynamical systems, topological dynamical system, dyadic development, purely discrete spectrum, coincidence condition, conjugacy map, generalized substitutions, biinfinite sequences Key Phrases - Capitalized Phrases (CAPs): (learn more)
Mendès France, The Chacon, The Hadamard, Bounded Gaps New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 5
books:
- Ergodic Theory (Cambridge Studies in Advanced Mathematics) by Karl E. Petersen in Back Matter (1), Back Matter (2), and Back Matter (3)
- Ergodic Theory (Grundlehren der mathematischen Wissenschaften) by I. P. Kornfeld in Back Matter (1), and Back Matter (2)
- Complex Systems (Nonlinear Phenomena and Complex Systems) by E. Goles in Back Matter
- Number Theory by Derek Holton in Back Matter
- Pure Mathematics: Detailed Solutions to Advanced Level Questions by D. Murray in Back Matter
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