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Substitution and Tiling Dynamics: Introduction to Self-inducing Structures = CIRM Jean-Morlet Chair, Fall 2017 /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Substitution and Tiling Dynamics: Introduction to Self-inducing Structures/ edited by Shigeki Akiyama, Pierre Arnoux.
其他題名:	CIRM Jean-Morlet Chair, Fall 2017 /
其他作者:	Arnoux, Pierre.
面頁冊數:	XIX, 456 p. 144 illus., 51 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Convex and Discrete Geometry. -
電子資源:	https://doi.org/10.1007/978-3-030-57666-0
ISBN:	9783030576660

Substitution and Tiling Dynamics: Introduction to Self-inducing Structures = CIRM Jean-Morlet Chair, Fall 2017 /
Substitution and Tiling Dynamics: Introduction to Self-inducing StructuresCIRM Jean-Morlet Chair, Fall 2017 /[electronic resource] :edited by Shigeki Akiyama, Pierre Arnoux. - 1st ed. 2020. - XIX, 456 p. 144 illus., 51 illus. in color.online resource. - Lecture Notes in Mathematics,22730075-8434 ;. - Lecture Notes in Mathematics,2144.

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.

ISBN: 9783030576660

Standard No.: 10.1007/978-3-030-57666-0doiSubjects--Topical Terms:

672138
Convex and Discrete Geometry.

LC Class. No.: QA313

Dewey Class. No.: 515.39

Substitution and Tiling Dynamics: Introduction to Self-inducing Structures = CIRM Jean-Morlet Chair, Fall 2017 /
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