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Mathematics of aperiodic order

Kellendonk, Johannes.

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Mathematics of aperiodic order

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Mathematics of aperiodic order/ edited by Johannes Kellendonk, Daniel Lenz, Jean Savinien.
other author:	Kellendonk, Johannes.
Published:	Basel :Springer Basel : : 2015.,
Description:	xii, 428 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
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:

952147
Aperiodic tilings.

LC Class. No.: QA640.72

Dewey Class. No.: 516.11

Mathematics of aperiodic order
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245 0 0 $a Mathematics of aperiodic order $h [electronic resource] / $c edited by Johannes Kellendonk, Daniel Lenz, Jean Savinien.
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300 $a xii, 428 p. : $b ill., digital ; $c 24 cm.
490 1 $a Progress in mathematics, $x 0743-1643 ; $v v.309
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 952147
650 0 $a Aperiodicity. $3 887785
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Convex and Discrete Geometry. $3 893686
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 891276
650 2 4 $a Operator Theory. $3 897311
650 2 4 $a Number Theory. $3 891078
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 891107
700 1 $a Kellendonk, Johannes. $3 2156824
700 1 $a Lenz, Daniel. $3 2156825
700 1 $a Savinien, Jean. $3 2156826
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Progress in mathematics ; $v v.295. $3 1566157
856 4 0 $u http://dx.doi.org/10.1007/978-3-0348-0903-0
950 $a Mathematics and Statistics (Springer-11649)