Mathematics of Aperiodic Order
What is order that is not based on simple repetition, that is, periodicity? How must atoms be arranged in a material so that it diffracts like a quasicrystal? How can we describe aperiodically ordered systems mathematically? Originally triggered by the –
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Johannes Kellendonk Daniel Lenz Jean Savinien Editors
Mathematics of Aperiodic Order
Progress in Mathematics Volume 309
Series Editors Hyman Bass, University of Michigan, Ann Arbor, USA Jiang-Hua Lu, The University of Hong Kong, Hong Kong SAR, China Joseph Oesterlé, Université Pierre et Marie Curie, Paris, France Yuri Tschinkel, Courant Institute of Mathematical Sciences, New York, USA
More information about this series at http://www.springer.com/series/4848
Johannes Kellendonk • Daniel Lenz • Jean Savinien Editors
Mathematics of Aperiodic Order
Editors Johannes Kellendonk Institut Camille Jordan Université Claude Bernard Lyon 1 Villeurbanne Cedex, France
Daniel Lenz Institut für Mathematik Friedrich-Schiller-Universität Jena Jena, Germany
Jean Savinien Institut Elie Cartan de Lorraine Université de Lorraine Metz Cedex 1, France
ISSN 0743-1643 ISSN 2296-505X (electronic) Progress in Mathematics ISBN 978-3-0348-0902-3 ISBN 978-3-0348-0903-0 (eBook) DOI 10.1007/978-3-0348-0903-0 Library of Congress Control Number: 2015942704 Mathematics Subject Classification (2010): 52C23, 37B50, 47A35, 11K70, 58B34 Springer Basel Heidelberg New York Dordrecht London © Springer Basel 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer Basel AG is part of Springer Science+Business Media (www.birkhauser-science.com)
Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1 Non-Periodic Systems with Continuous Diffraction Measures M. Baake, M. Birkner and U. Grimm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
2 On the Pisot Substitution Conjecture S. Akiyama, M. Barge, V. Berth´e, J.-Y. Lee and A. Siegel . . . . . . . . . . . .
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3 Cohomology of Hierarchical Tilings L. Sadun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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4 Spaces of Projection M
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