*(English)*Zbl 1014.11015

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

##### MSC:

11B85 | Automata sequences |

11-02 | Research monographs (number theory) |

37-02 | Research exposition (Dynamical systems and ergodic theory) |

05-02 | Research monographs (combinatorics) |

68Q45 | Formal languages and automata |

68R15 | Combinatorics on words |

11A55 | Continued fractions (number-theoretic results) |

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 |

05A17 | Partitions of integers (combinatorics) |