| Description |
1 online resource (xix, 456 pages) : illustrations (some color) |
| Series |
Lecture notes in mathematics, 0075-8434 ; volume 2273 |
|
CIRM Jean-Morlet series |
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Lecture notes in mathematics (Springer-Verlag) ; 2273. 0075-8434
|
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CIRM Jean-Morlet series
|
| Contents |
Delone sets and dynamical systems -- Introduction to hierarchical tiling dynamical systems -- S-adic sequences : dynamics, arithmetic, and geometry -- Operators and Algebras for Aperiodic Tilings -- From games to morphisms -- The Undecidability of the Domino Problem -- Renormalisation for block substitutions -- Yet another characterization of the Pisot conjecture |
| Summary |
This book presents a panorama of recent developments in the theory of tilings and related dynamical systems. It contains an expanded version of courses given in 2017 at the research school associated with the Jean-Morlet chair program. Tilings have been designed, used and studied for centuries in various contexts. This field grew significantly after the discovery of aperiodic self-similar tilings in the 60s, linked to the proof of the undecidability of the Domino problem, and was driven futher by Dan Shechtman's discovery of quasicrystals in 1984. Tiling problems establish a bridge between the mutually influential fields of geometry, dynamical systems, aperiodic order, computer science, number theory, algebra and logic. The main properties of tiling dynamical systems are covered, with expositions on recent results in self-similarity (and its generalizations, fusions rules and S-adic systems), algebraic developments connected to physics, games and undecidability questions, and the spectrum of substitution tilings |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed February 12, 2021) |
| Subject |
Tiling (Mathematics)
|
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Sequences (Mathematics)
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Aperiodicity.
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Topological dynamics.
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Sucesiones (Matemáticas)
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Dinámica topológica
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Topological dynamics
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Tiling (Mathematics)
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Sequences (Mathematics)
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Aperiodicity
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Computer science
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Convex geometry
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Discrete geometry
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Dynamics
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Ergodic theory
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Vibration
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| Form |
Electronic book
|
| Author |
Akiyama, Shigeki, editor
|
|
Arnoux, P. (Pierre), editor.
|
| ISBN |
9783030576660 |
|
3030576663 |
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