Beyond Quasicrystals

This topical volume gives a presentation of geometric and topological properties of quasicrystals and studies diffraction theory of long-range objects with non-trivial order. The goal was to construct a rigorous frame for sequences generation and Fourier analysis. The book is ideal for experimentalists as a manual on the theoretical background of their work.

Inhalt
Quasicrystals ....- Course 1 Quasicrystals, diophantine approximation and algebraic numbers.- Course 2 The pentacrystals.- Course 3 Elements of a multimetrical crystallography.- Course 4 Non-commutative models for quasicrystals.- Course 5 From quasiperiodic to more complex systems.- Course 6 Matching rules and quasiperiodicity: the octagonal tilings.- Course 7 A mechanism for diffusion in quasicrystals.- Course 8 Experimental aspects of the structure analysis of aperiodic materials.- Course 9 Scattering on aperiodic superlattices.- Course 10 Defects in quasicrystals, in systems with deterministic disorder and in amorphous materials.- ...and Beyond.- Course 11 Automata and automatic sequences.- Course 12 Spectral study of automatic and substitutive sequences.- Course 13 Random and automatic walks.- Course 14 Singular words, invertible substitutions and local isomorphisms.- Course 15 Entropy in deterministic and random systems.- Course 16 Trace maps.- Course 17 Schrödinger difference equation with deterministic ergodic potentials.- Course 18 Schrödinger equation in a hierarchical potential.- Course 19 Introduction to multifractal analysis.- Appendix 1. Legendre transforms.- Appendix 2. Large deviations.- Annexes.- Current deterministic sequences.- Extra references.

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