05338nam 22008655 450 991029977530332120200629192547.03-0348-0903-410.1007/978-3-0348-0903-0(CKB)3710000000422102(EBL)2096880(SSID)ssj0001524994(PQKBManifestationID)11816957(PQKBTitleCode)TC0001524994(PQKBWorkID)11485285(PQKB)11043014(DE-He213)978-3-0348-0903-0(MiAaPQ)EBC2096880(PPN)186400411(EXLCZ)99371000000042210220150605d2015 u| 0engur|n|---|||||txtccrMathematics of Aperiodic Order /edited by Johannes Kellendonk, Daniel Lenz, Jean Savinien1st ed. 2015.Basel :Springer Basel :Imprint: Birkhäuser,2015.1 online resource (438 p.)Progress in Mathematics,0743-1643 ;309Description based upon print version of record.3-0348-0902-6 Includes bibliographical references at the end of each chapters.Preface -- 1.M. Baake, M. Birkner and U. Grimm: Non-Periodic Systems with Continuous Diffraction Measures -- 2.S. Akiyama, M. Barge, V. Berthé, 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 Schrödinger 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 Schrödinger operators, and connections to arithmetic number theory.Progress in Mathematics,0743-1643 ;309Convex geometry Discrete geometryDynamicsErgodic theoryOperator theoryNumber theoryGlobal analysis (Mathematics)Manifolds (Mathematics)Convex and Discrete Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21014Dynamical Systems and Ergodic Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M1204XOperator Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M12139Number Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M25001Global Analysis and Analysis on Manifoldshttps://scigraph.springernature.com/ontologies/product-market-codes/M12082Convex geometry .Discrete geometry.Dynamics.Ergodic theory.Operator theory.Number theory.Global analysis (Mathematics).Manifolds (Mathematics).Convex and Discrete Geometry.Dynamical Systems and Ergodic Theory.Operator Theory.Number Theory.Global Analysis and Analysis on Manifolds.512.25516.11Kellendonk Johannesedthttp://id.loc.gov/vocabulary/relators/edtLenz Danieledthttp://id.loc.gov/vocabulary/relators/edtSavinien Jeanedthttp://id.loc.gov/vocabulary/relators/edtMiAaPQMiAaPQMiAaPQBOOK9910299775303321Mathematics of aperiodic order1522481UNINA