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Substitutions in dynamics, arithmetics and combinatorics. (English) Zbl 1014.11015
Lecture Notes in Mathematics. 1794. Berlin: Springer. xv, 402 p. EUR 57.95/net; sFr. 96.50; £40.50; $ 76.80 (2002).
This collective book, published under the pseudonym N. Pytheas Fogg, based on courses given by the authors in several universities and during several summer schools, addresses the study of substitutions from the triple point of view of dynamics, arithmetics, and combinatorics: from transcendence to partitions, from symbolic (substitutive) dynamical systems to Sturmian sequences, from spectral theory to Diophantine approximations and fractals, from invertible substitutions to polynomial substitutive dynamical systems, from piecewise linear transformations of the unit interval to Cantor sets. The twelve chapters written by ten authors and the appendix written by an eleventh author give an eclectic variety of themes that is both pleasant to read and filled with many results and ideas.
The book ends with a large bibliography of 469 items. Actually the numbers corresponding to references quoted in the chapters after the first are shifted by 1 roughly after [100], but the correctly numbered bibliography is freely accessible at http://link.springer.de/series/lnm.

MSC:
11B85 Automata sequences
11-02 Research exposition (monographs, survey articles) pertaining to number theory
37-02 Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory
05-02 Research exposition (monographs, survey articles) pertaining to combinatorics
68Q45 Formal languages and automata
68R15 Combinatorics on words
11A55 Continued fractions
11A63 Radix representation; digital problems
11J70 Continued fractions and generalizations
37B10 Symbolic dynamics
28D99 Measure-theoretic ergodic theory
37A45 Relations of ergodic theory with number theory and harmonic analysis (MSC2010)
05A17 Combinatorial aspects of partitions of integers
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