an:01823664
Zbl 1014.11015
Fogg, N. Pytheas (ed.); Berth??, Val??rie (ed.); Ferenczi, S??bastien (ed.); Mauduit, Christian (ed.); Siegel, A. (ed.)
Substitutions in dynamics, arithmetics and combinatorics
EN
Lecture Notes in Mathematics. 1794. Berlin: Springer. xv, 402 p. EUR 57.95/net; sFr. 96.50; \textsterling 40.50; \$ 76.80 (2002).
00379061
2002
b
11B85 11-02 37-02 05-02 68Q45 68R15 11A55 11A63 11J70 37B10 28D99 37A45 05A17
substitutions; transcendence; partitions; dynamical systems; Sturmian sequences; spectral theory; Diophantine approximations; fractals; invertible substitutions; polynomial substitutive dynamical systems; piecewise linear transformations of the unit interval; Cantor sets
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 \texttt{http://link.springer.de/series/lnm}.
Jean-Paul Allouche (Orsay)