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Mathematics of aperiodic order

Kellendonk, Johannes.

Mathematics of aperiodic order

Record Type:	Electronic resources : Monograph/item
Title/Author:	Mathematics of aperiodic orderedited by Johannes Kellendonk, Daniel Lenz, Jean Savinien.
other author:	Kellendonk, Johannes.
Published:	Basel :Springer Basel :2015.
Description:	xii, 428 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Aperiodic tilings.
Online resource:	http://dx.doi.org/10.1007/978-3-0348-0903-0
ISBN:	9783034809030 (electronic bk.)

Mathematics of aperiodic order
Mathematics of aperiodic order[electronic resource] /edited by Johannes Kellendonk, Daniel Lenz, Jean Savinien. - Basel :Springer Basel :2015. - xii, 428 p. :ill., digital ;24 cm. - Progress in mathematics,v.3090743-1643 ;. - Progress in mathematics ;v.295..

Preface -- 1.M. Baake, M. Birkner and U. Grimm: Non-Periodic Systems with Continuous Diffraction Measures -- 2.S. Akiyama, M. Barge, V. Berthe, J.-Y. Lee and A. Siegel: On the Pisot Substitution Conjecture -- 3. L. Sadun: Cohomology of Hierarchical Tilings -- 4.J. Hunton: Spaces of Projection Method Patterns and their Cohomology -- 5.J.-B. Aujogue, M. Barge, J. Kellendonk, D. Lenz: Equicontinuous Factors, Proximality and Ellis Semigroup for Delone Sets -- 6.J. Aliste-Prieto, D. Coronel, M.I. Cortez, F. Durand and S. Petite: Linearly Repetitive Delone Sets -- 7.N. Priebe Frank: Tilings with Infinite Local Complexity -- 8. A.Julien, J. Kellendonk and J. Savinien: On the Noncommutative Geometry of Tilings -- 9.D. Damanik, M. Embree and A. Gorodetski: Spectral Properties of Schrodinger Operators Arising in the Study of Quasicrystals -- 10.S. Puzynina and L.Q. Zamboni: Additive Properties of Sets and Substitutive Dynamics -- 11.J.V. Bellissard: Delone Sets and Material Science: a Program.

What is order that is not based on simple repetition, that is, periodicity? How must atoms be arranged in a material so that it diffracts like a quasicrystal? How can we describe aperiodically ordered systems mathematically? Originally triggered by the - later Nobel prize-winning - discovery of quasicrystals, the investigation of aperiodic order has since become a well-established and rapidly evolving field of mathematical research with close ties to a surprising variety of branches of mathematics and physics. This book offers an overview of the state of the art in the field of aperiodic order, presented in carefully selected authoritative surveys. It is intended for non-experts with a general background in mathematics, theoretical physics or computer science, and offers a highly accessible source of first-hand information for all those interested in this rich and exciting field. Topics covered include the mathematical theory of diffraction, the dynamical systems of tilings or Delone sets, their cohomology and non-commutative geometry, the Pisot substitution conjecture, aperiodic Schrodinger operators, and connections to arithmetic number theory.

ISBN: 9783034809030 (electronic bk.)

Standard No.: 10.1007/978-3-0348-0903-0doiSubjects--Topical Terms:

726876
Aperiodic tilings.

LC Class. No.: QA640.72

Dewey Class. No.: 516.11

Mathematics of aperiodic order
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505 0 $a Preface -- 1.M. Baake, M. Birkner and U. Grimm: Non-Periodic Systems with Continuous Diffraction Measures -- 2.S. Akiyama, M. Barge, V. Berthe, J.-Y. Lee and A. Siegel: On the Pisot Substitution Conjecture -- 3. L. Sadun: Cohomology of Hierarchical Tilings -- 4.J. Hunton: Spaces of Projection Method Patterns and their Cohomology -- 5.J.-B. Aujogue, M. Barge, J. Kellendonk, D. Lenz: Equicontinuous Factors, Proximality and Ellis Semigroup for Delone Sets -- 6.J. Aliste-Prieto, D. Coronel, M.I. Cortez, F. Durand and S. Petite: Linearly Repetitive Delone Sets -- 7.N. Priebe Frank: Tilings with Infinite Local Complexity -- 8. A.Julien, J. Kellendonk and J. Savinien: On the Noncommutative Geometry of Tilings -- 9.D. Damanik, M. Embree and A. Gorodetski: Spectral Properties of Schrodinger Operators Arising in the Study of Quasicrystals -- 10.S. Puzynina and L.Q. Zamboni: Additive Properties of Sets and Substitutive Dynamics -- 11.J.V. Bellissard: Delone Sets and Material Science: a Program.
520 $a What is order that is not based on simple repetition, that is, periodicity? How must atoms be arranged in a material so that it diffracts like a quasicrystal? How can we describe aperiodically ordered systems mathematically? Originally triggered by the - later Nobel prize-winning - discovery of quasicrystals, the investigation of aperiodic order has since become a well-established and rapidly evolving field of mathematical research with close ties to a surprising variety of branches of mathematics and physics. This book offers an overview of the state of the art in the field of aperiodic order, presented in carefully selected authoritative surveys. It is intended for non-experts with a general background in mathematics, theoretical physics or computer science, and offers a highly accessible source of first-hand information for all those interested in this rich and exciting field. Topics covered include the mathematical theory of diffraction, the dynamical systems of tilings or Delone sets, their cohomology and non-commutative geometry, the Pisot substitution conjecture, aperiodic Schrodinger operators, and connections to arithmetic number theory.
650 0 $a Aperiodic tilings. $3 726876
650 0 $a Aperiodicity. $3 272982
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Convex and Discrete Geometry. $3 277230
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 273794
650 2 4 $a Operator Theory. $3 274795
650 2 4 $a Number Theory. $3 274059
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 273786
700 1 $a Kellendonk, Johannes. $3 726874
700 1 $a Lenz, Daniel. $3 515958
700 1 $a Savinien, Jean. $3 726875
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