TY  - BOOK
AU  - Fogg,N.Pytheas
AU  - Berthé,Valéré
AU  - Ferenczi,Sébastien
AU  - Mauduit,Christian
AU  - Siegel,Anne
ED  - SpringerLink (Online service)
TI  - Substitutions in Dynamics, Arithmetics and Combinatorics
T2  - Lecture Notes in Mathematics,
SN  - 9783540457145
AV  - QA241-247.5 
U1  - 512.7 23
PY  - 2002///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Computer science
KW  - Differentiable dynamical systems
KW  - Sequences (Mathematics)
KW  - Number theory
KW  - Number Theory
KW  - Real Functions
KW  - Dynamical Systems and Ergodic Theory
KW  - Sequences, Series, Summability
KW  - Computation by Abstract Devices
KW  - Mathematical Logic and Formal Languages
N1  - 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)
N2  - 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
UR  - http://dx.doi.org/10.1007/b13861
ER  -