Substitutions in Dynamics, Arithmetics and Combinatorics

• Main Author: Pytheas Fogg, N. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Other Authors: Berthé, Valerie (Editor, http://id.loc.gov/vocabulary/relators/edt), Ferenczi, Sebastien (Editor, http://id.loc.gov/vocabulary/relators/edt), Mauduit, Christian (Editor, http://id.loc.gov/vocabulary/relators/edt), Siegel, Anne (Editor, http://id.loc.gov/vocabulary/relators/edt)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002.
• Edition: 1st ed. 2002.
• Series: Lecture Notes in Mathematics, 1794
• Subjects: Number theory.; Functions of real variables.; Dynamics.; Ergodic theory.; Sequences (Mathematics).; Computers.; Mathematical logic.; Number Theory.; Real Functions.; Dynamical Systems and Ergodic Theory.; Sequences, Series, Summability.; Computation by Abstract Devices.; Mathematical Logic and Formal Languages.

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 itera...

Table of Contents:

• Basic notions on substitutions
• Basic notions on substitutions
• Arithmetics and combinatorics of substitutions
• Substitutions, arithmetic and finite automata: an introduction
• Automatic sequences and transcendence
• Substitutions and partitions of the set of positive integers
• Dynamics of substitutions
• Substitutions and symbolic dynamical systems
• Sturmian Sequences
• Spectral theory and geometric representation of substitutions
• Diophantine approximations, substitutions, and fractals
• Extensions to free groups and interval transformations
• Infinite words generated by invertible substitutions
• Polynomial dynamical systems associated with substitutions
• Piecewise linear transformations of the unit interval and Cantor sets
• Some open problems
• A. Undecomposable matrices in dimension 3 (by J. Rivat).