Substitutions in Dynamics, Arithmetics and Combinatorics

N. Pytheas Fogg (Autor)

Valerie Berthé, Sebastien Ferenczi, Christian Mauduit, Anne Siegel (Herausgeber)

Buch | Softcover

XX, 404 Seiten

2002 | 2002
Springer Berlin (Verlag)
978-3-540-44141-0 (ISBN)

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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.

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).

Erscheint lt. Verlag	23.9.2002
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XX, 404 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	625 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Alphabet • Arithmetik • Automata • automata sequences • combinatorics • Combinatorics on Words • Diophantine approximation • Dynamical Systems • Dynamik • ergodic theory • Fractal • graph theory • Kombinatorik • Partition • substitutive dynamical systems • symbolic dynamics
ISBN-10	3-540-44141-7 / 3540441417
ISBN-13	978-3-540-44141-0 / 9783540441410
Zustand	Neuware