LEADER 05338nam 22008655 450 001 9910299775303321 005 20200629192547.0 010 $a3-0348-0903-4 024 7 $a10.1007/978-3-0348-0903-0 035 $a(CKB)3710000000422102 035 $a(EBL)2096880 035 $a(SSID)ssj0001524994 035 $a(PQKBManifestationID)11816957 035 $a(PQKBTitleCode)TC0001524994 035 $a(PQKBWorkID)11485285 035 $a(PQKB)11043014 035 $a(DE-He213)978-3-0348-0903-0 035 $a(MiAaPQ)EBC2096880 035 $a(PPN)186400411 035 $a(EXLCZ)993710000000422102 100 $a20150605d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMathematics of Aperiodic Order /$fedited by Johannes Kellendonk, Daniel Lenz, Jean Savinien 205 $a1st ed. 2015. 210 1$aBasel :$cSpringer Basel :$cImprint: Birkhäuser,$d2015. 215 $a1 online resource (438 p.) 225 1 $aProgress in Mathematics,$x0743-1643 ;$v309 300 $aDescription based upon print version of record. 311 $a3-0348-0902-6 320 $aIncludes bibliographical references at the end of each chapters. 327 $aPreface -- 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. 330 $aWhat is order that is not based on simple repetition, that is, periodicity? How must atoms be arranged in a material so that it diffracts like a quasicrystal? How can we describe aperiodically ordered systems mathematically? Originally triggered by the ? later Nobel prize-winning ? discovery of quasicrystals, the investigation of aperiodic order has since become a well-established and rapidly evolving field of mathematical research with close ties to a surprising variety of branches of mathematics and physics. This book offers an overview of the state of the art in the field of aperiodic order, presented in carefully selected authoritative surveys. It is intended for non-experts with a general background in mathematics, theoretical physics or computer science, and offers a highly accessible source of first-hand information for all those interested in this rich and exciting field. Topics covered include the mathematical theory of diffraction, the dynamical systems of tilings or Delone sets, their cohomology and non-commutative geometry, the Pisot substitution conjecture, aperiodic Schrödinger operators, and connections to arithmetic number theory. 410 0$aProgress in Mathematics,$x0743-1643 ;$v309 606 $aConvex geometry  606 $aDiscrete geometry 606 $aDynamics 606 $aErgodic theory 606 $aOperator theory 606 $aNumber theory 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aConvex and Discrete Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21014 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 606 $aGlobal Analysis and Analysis on Manifolds$3https://scigraph.springernature.com/ontologies/product-market-codes/M12082 615 0$aConvex geometry . 615 0$aDiscrete geometry. 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aOperator theory. 615 0$aNumber theory. 615 0$aGlobal analysis (Mathematics). 615 0$aManifolds (Mathematics). 615 14$aConvex and Discrete Geometry. 615 24$aDynamical Systems and Ergodic Theory. 615 24$aOperator Theory. 615 24$aNumber Theory. 615 24$aGlobal Analysis and Analysis on Manifolds. 676 $a512.25 676 $a516.11 702 $aKellendonk$b Johannes$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aLenz$b Daniel$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aSavinien$b Jean$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299775303321 996 $aMathematics of aperiodic order$91522481 997 $aUNINA