Overview
- Features beautifully illustrated lectures on self-inducing structures with cutting-edge results related to substitutions and tilings
- Provides an easy introduction to S-adic systems and self-affine tilings
- Includes chapters on games and undecidability questions and on the spectrum of substitution tilings
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2273)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Editors and Affiliations
Bibliographic Information
Book Title: Substitution and Tiling Dynamics: Introduction to Self-inducing Structures
Book Subtitle: CIRM Jean-Morlet Chair, Fall 2017
Editors: Shigeki Akiyama, Pierre Arnoux
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-030-57666-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-57665-3Published: 06 December 2020
eBook ISBN: 978-3-030-57666-0Published: 05 December 2020
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XIX, 456
Number of Illustrations: 93 b/w illustrations, 51 illustrations in colour
Additional Information: Jointly published with Société Mathématique de France (SMF), Paris, France
Topics: Dynamical Systems and Ergodic Theory, Vibration, Dynamical Systems, Control, Computer Science, general, Convex and Discrete Geometry