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＜電子ブック＞
Substitution and Tiling Dynamics: Introduction to Self-inducing Structures : CIRM Jean-Morlet Chair, Fall 2017 / edited by Shigeki Akiyama, Pierre Arnoux
(Lecture Notes in Mathematics. ISSN:16179692 ; 2273)

版	1st ed. 2020.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2020
本文言語	英語
大きさ	XIX, 456 p. 144 illus., 51 illus. in color : online resource
著者標目	Akiyama, Shigeki editor Arnoux, Pierre editor SpringerLink (Online service)
件　名	LCSH:Dynamical systems LCSH:Multibody systems LCSH:Vibration LCSH:Mechanics, Applied LCSH:Computer science LCSH:Convex geometry  LCSH:Discrete geometry FREE:Dynamical Systems FREE:Multibody Systems and Mechanical Vibrations FREE:Computer Science FREE:Convex and Discrete Geometry
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-030-57666-0

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