✍ Scribed by Fogg, N. Pytheas; Berthé, Valéré; Ferenczi, Sébastien; Mauduit, Christian; Siegel, Anne
No coin nor oath required. For personal study only.
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. Preface -- 1. Basic Notions On Substitutions -- Part I: Arithmetics And Combinatorics -- 2. Substitutions, Arithmetic And Finite Automata: An Introduction -- 3. Automatic Sequences And Transcendence -- 4. Substitutions And Partitions Of The Set Of Positive Integers -- Part Ii: Dynamics Of Substitutions -- 5. Substitutions And Symbolic Dynamical Systems -- 6. Sturmian Sequences -- 7. Spectral Theory And Geometric Representation Of Substitutions -- 8. Diophantine Approximations, Substitutions, And Fractals -- Part Iii: Extensions To Free Groups And Interval Transformations -- 9. Infinite Words Generated By Invertible Substitutions -- 10. Polynomial Dynamical Systems Associated With Substitutions -- 11. Piecewise Linear Transformations Of The Unit Interval And Cantor Sets -- 12. Some Open Problems -- A. Undecomposable Matrices In Dimension 3 -- References -- Index. N. Pytheas Fogg ; Editors, V. Berthé ... [et Al.]. Includes Bibliographical References (p. [377]-397) And Index. Also Available In An Electronic Version.
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