Quasicrystals and Discrete Geometry ( Fields Institute Monographs )

Publication series :Fields Institute Monographs

Author: Jiřì Patera  

Publisher: American Mathematical Society‎

Publication year: 1998

E-ISBN: 9781470431372

P-ISBN(Hardback):  9780821806821

Subject: O152 group theory

Keyword: 暂无分类

Language: ENG

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Quasicrystals and Discrete Geometry

Description

The common topic of the eleven articles in this volume is ordered aperiodic systems realized either as point sets with the Delone property or as tilings of a Euclidean space. This emerging field of study is found at the crossroads of algebra, geometry, Fourier analysis, number theory, crystallography, and theoretical physics. The volume brings together contributions by leading specialists. Important advances in understanding the foundations of this new field are presented.

Chapter

Title page

Contents

Preface

Similarity submodules and semigroups

Pisot-cyclotomic quasilattices and their symmetry semigroups

Three possible branches of determinate modular generalization of crystallography

Non-crystallographic root systems

Upper bounds for the lengths of bridges based on Delone sets

The local theorem for tilings

Uniform distribution and the projection method

One corona is enough for the Euclidean plane

Cut-and-project sets in locally compact Abelian groups

Spectrum of dynamical systems arising from Delone sets

Non-locality and aperiodicity of 𝑑-dimensional tilings

Index

Back Cover

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