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    This (lowercase (translateProductType product.productType)) has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Baake, Michael Grimm, Uwe and Mañibo, Neil 2018. Spectral analysis of a family of binary inflation rules. Letters in Mathematical Physics,

    FERNIQUE, THOMAS and SABLIK, MATHIEU 2018. Weak colored local rules for planar tilings. Ergodic Theory and Dynamical Systems, p. 1.

    Haynes, Alan Koivusalo, Henna and Walton, James 2018. A characterization of linearly repetitive cut and project sets. Nonlinearity, Vol. 31, Issue. 2, p. 515.

    Madison, A.E. 2018. Constructing Penrose-like tilings with 7-fold symmetry. Structural Chemistry, Vol. 29, Issue. 2, p. 645.

    KELLER, GERHARD and RICHARD, CHRISTOPH 2018. Dynamics on the graph of the torus parametrization. Ergodic Theory and Dynamical Systems, Vol. 38, Issue. 03, p. 1048.

    Frettlöh, Dirk and Garber, Alexey 2018. Weighted $$1\times 1$$1×1 Cut-and-Project Sets in Bounded Distance to a Lattice. Discrete & Computational Geometry,

    Björklund, Michael Hartnick, Tobias and Pogorzelski, Felix 2018. Aperiodic order and spherical diffraction, I: auto-correlation of regular model sets. Proceedings of the London Mathematical Society, Vol. 116, Issue. 4, p. 957.

    Nekrashevych, Volodymyr 2018. Palindromic subshifts and simple periodic groups of intermediate growth. Annals of Mathematics, Vol. 187, Issue. 3, p. 667.

    Baake, Michael and Grimm, Uwe 2017. Diffraction of a binary non-Pisot inflation tiling. Journal of Physics: Conference Series, Vol. 809, Issue. , p. 012026.

    Wolff, Gil and Levine, Dov 2017. Diffuse scattering and atomic order. EPL (Europhysics Letters), Vol. 117, Issue. 3, p. 36001.

    Roth, Johannes 2017. Properties of quasiperiodic functions. Journal of Physics: Condensed Matter, Vol. 29, Issue. 18, p. 184003.

    Kellendonk, Johannes and Sadun, Lorenzo 2017. Conjugacies of model sets. Discrete and Continuous Dynamical Systems, Vol. 37, Issue. 7, p. 3805.

    Maciá, Enrique 2017. Spectral Classification of One-Dimensional Binary Aperiodic Crystals: An Algebraic Approach. Annalen der Physik, Vol. 529, Issue. 10, p. 1700079.

    Eschenburg, J.-H. and Rivertz, H. J. 2017. The complete cartwheel tiling. Journal of Geometry, Vol. 108, Issue. 2, p. 703.

    Mañibo, Neil 2017. Lyapunov exponents for binary substitutions of constant length. Journal of Mathematical Physics, Vol. 58, Issue. 11, p. 113504.

    Lee, Jeong-Yup and Moody, Robert V. 2017. On the Penrose and Taylor–Socolar hexagonal tilings. Acta Crystallographica Section A Foundations and Advances, Vol. 73, Issue. 3, p. 246.

    Yassawi, Reem Roberts, John A. G. and Baake, Michael 2017. Reversing and extended symmetries of shift spaces. Discrete and Continuous Dynamical Systems, Vol. 38, Issue. 2, p. 835.

    Dreher, F. Kesseböhmer, M. Mosbach, A. Samuel, T. and Steffens, M. 2017. Regularity of aperiodic minimal subshifts. Bulletin of Mathematical Sciences,

    Ben-Abraham, S I and Flom, D 2017. Brick tiling. Journal of Physics: Conference Series, Vol. 809, Issue. , p. 012024.

    LENZ, DANIEL and MOODY, ROBERT V. 2017. Stationary processes and pure point diffraction. Ergodic Theory and Dynamical Systems, Vol. 37, Issue. 08, p. 2597.

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  • Volume 1: A Mathematical Invitation
  • Michael Baake, Universität Bielefeld, Germany , Uwe Grimm, The Open University, Milton Keynes

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    Aperiodic Order
    • Online ISBN: 9781139025256
    • Book DOI: https://doi.org/10.1017/CBO9781139025256
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Book description

Quasicrystals are non-periodic solids that were discovered in 1982 by Dan Shechtman, Nobel Prize Laureate in Chemistry 2011. The underlying mathematics, known as the theory of aperiodic order, is the subject of this comprehensive multi-volume series. This first volume provides a graduate-level introduction to the many facets of this relatively new area of mathematics. Special attention is given to methods from algebra, discrete geometry and harmonic analysis, while the main focus is on topics motivated by physics and crystallography. In particular, the authors provide a systematic exposition of the mathematical theory of kinematic diffraction. Numerous illustrations and worked-out examples help the reader to bridge the gap between theory and application. The authors also point to more advanced topics to show how the theory interacts with other areas of pure and applied mathematics.

Reviews

'Mathematicians add hypotheses to theorems either to bar known monsters or provisionally to enable proof, pending better ideas that lead to more general results … Monsters no more, aperiodic filings have joined mainstream mathematics, and undergraduates drawn here by beautiful graphics will find themselves initiated into algebraic number theory, Lie theory, ergodic theory, dynamical systems, finite-state automata, Fourier analysis, and more.'

D. V. Feldman - University of New Hampshire

'Aperiodic Order is a comprehensive introduction to this relatively new and multidisciplinary field. Sparked by Dan Shechtman’s discovery of quasicrystals in 1982, which earned him the 2011 Nobel Prize in Chemistry, the field incorporates crystallography, discrete geometry, dynamical systems, harmonic analysis, mathematical diffraction theory, and more. Because the field spans such disparate fields, advances by one group often go unnoticed by the other. An important goal of this book is to remedy this by unifying and contextualizing results and providing a common language for researchers. … Readers who want to follow up on any details can certainly find a reference in the nearly 30 pages of bibliographic entries. Full of examples, construction techniques, and an array of analytic tools, this book is an outstanding resource for those hoping to enter the field, yet also contains plenty of useful information for seasoned experts.'

Natalie Priebe Frank Source: Mathematical Association of America

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