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

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Shigeki Akiyama Pierre Arnoux

Substitution and Tiling Dynamics

Introduction to Self-inducing Structures: CIRM Jean-Morlet Chair, Fall 2017

Shigeki Akiyama, Pierre Arnoux

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English

Springer Nature Switzerland AG
06 December 2020

Discrete mathematics; Algebraic geometry; Non-linear science; Dynamics & vibration; Computer science

Series: Lecture Notes in Mathematics

Summary
Details

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.

Edited by: Shigeki Akiyama, Pierre Arnoux
Imprint: Springer Nature Switzerland AG
Country of Publication: Switzerland
Edition: 1st ed. 2020
Volume: 2273
Dimensions: Height: 235mm, Width: 155mm,
Weight: 724g
ISBN: 9783030576653
ISBN 10: 3030576655
Series: Lecture Notes in Mathematics
Pages: 456
Publication Date: 06 December 2020
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active