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Substitution and tiling dynamicsintr...

Akiyama, Shigeki.

Substitution and tiling dynamicsintroduction to self-inducing structures : CIRM Jean-Morlet chair, Fall 2017 /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Substitution and tiling dynamicsedited by Shigeki Akiyama, Pierre Arnoux.
Reminder of title:	introduction to self-inducing structures : CIRM Jean-Morlet chair, Fall 2017 /
other author:	Akiyama, Shigeki.
Published:	Cham :Springer International Publishing :2020.
Description:	xix, 456 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Tiling (Mathematics)
Online resource:	https://doi.org/10.1007/978-3-030-57666-0
ISBN:	9783030576660$q(electronic bk.)

Substitution and tiling dynamicsintroduction to self-inducing structures : CIRM Jean-Morlet chair, Fall 2017 /
Substitution and tiling dynamicsintroduction to self-inducing structures : CIRM Jean-Morlet chair, Fall 2017 /[electronic resource] :edited by Shigeki Akiyama, Pierre Arnoux. - Cham :Springer International Publishing :2020. - xix, 456 p. :ill. (some col.), digital ;24 cm. - Lecture notes in mathematics,v.22730075-8434 ;. - Lecture notes in mathematics ;2035..

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$q(electronic bk.)

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

189530
Tiling (Mathematics)

LC Class. No.: QA313 / .S837 2020

Dewey Class. No.: 515.39

Substitution and tiling dynamicsintroduction to self-inducing structures : CIRM Jean-Morlet chair, Fall 2017 /
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490 1 $a Lecture notes in mathematics, $x 0075-8434 ; $v v.2273
505 0 $a 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.
520 $a 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.
650 0 $a Tiling (Mathematics) $3 189530
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650 0 $a Aperiodicity. $3 272982
650 0 $a Topological dynamics. $3 468099
650 1 4 $a Dynamical Systems and Ergodic Theory. $3 273794
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650 2 4 $a Computer Science, general. $3 274540
650 2 4 $a Convex and Discrete Geometry. $3 277230
700 1 $a Akiyama, Shigeki. $3 883107
700 1 $a Arnoux, Pierre. $3 883108
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