Beyond quasicrystals. Papers of the winter school, Les Houches, France, March 7-18, 1994. (English) Zbl 0880.00009

Berlin: Springer-Verlag. Les Ulis: Les Editions de Physique. xvi, 619 p. (1995).

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This collection of articles grew out of a Winter School at Les Houches which concentrated on mathematical and physical aspects of quasicrystals and – more generally – of all kinds of ordered structures related to them. The first half of the book covers number theoretic and crystallographic approaches to quasicrystals, examples, matching rules, diffusion and scattering, structure analysis, deflects and the relation to more complex systems. The second part deals with automatic sequences and their aspects, such as spectral theory, entropy, substitution rules, trace maps, and Schrödinger equation for such systems. Most articles have a review character but also contain advanced material that is hard to collect from other sources. As such, this book is a good starting point to the more theoretical aspects of non-periodically ordered structures. Articles of wider mathematical interest will be reviewed individually.

Reviewer: M.Baake (Tübingen)

MSC:

00A79	Physics
00B25	Proceedings of conferences of miscellaneous specific interest
82-06	Proceedings, conferences, collections, etc. pertaining to statistical mechanics
82D25	Statistical mechanics of crystals
11B85	Automata sequences

Keywords:

Papers; Winter School; Quasicrystals; Les Houches (France); quasicrystals; automatic sequences; spectral theory; entropy; substitution rules; trace maps; Schrödinger equation