LEADER 02980oam 2200505 450 001 996418192803316 005 20221219230859.0 010 $a3-030-57666-3 024 7 $a10.1007/978-3-030-57666-0 035 $a(OCoLC)1238199542 035 $a(CKB)4100000011643570 035 $a(DE-He213)978-3-030-57666-0 035 $a(MiAaPQ)EBC6421115 035 $a(PPN)251090396 035 $a(EXLCZ)994100000011643570 100 $a20210529d2020 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aSubstitution and tiling dynamics $eintroduction to self-inducing structures : CIRM Jean-Morlet Chair, Fall 2017 /$fShigeki Akiyama, Pierre Arnoux, editors 205 $a1st ed. 2020. 210 1$aCham, Switzerland :$cSpringer,$d[2020] 210 4$d©2020 215 $a1 online resource (XIX, 456 p. 144 illus., 51 illus. in color.) 225 0 $aLecture Notes in Mathematics,$x1617-9692 ;$vVolume 2273 311 $a3-030-57665-5 327 $aDelone sets and dynamical systems -- Introduction to hierarchical tiling dynamical systems -- S-adic sequences : dynamics, arithmetic, and geometry -- Operators and Algebras for Aperiodic Tilings -- From games to morphisms -- The Undecidability of the Domino Problem -- Renormalisation for block substitutions -- Yet another characterization of the Pisot conjecture. 330 $aThis book presents a panorama of recent developments in the theory of tilings and related dynamical systems. It contains an expanded version of courses given in 2017 at the research school associated with the Jean-Morlet chair program. Tilings have been designed, used and studied for centuries in various contexts. This field grew significantly after the discovery of aperiodic self-similar tilings in the 60s, linked to the proof of the undecidability of the Domino problem, and was driven futher by Dan Shechtman's discovery of quasicrystals in 1984. Tiling problems establish a bridge between the mutually influential fields of geometry, dynamical systems, aperiodic order, computer science, number theory, algebra and logic. The main properties of tiling dynamical systems are covered, with expositions on recent results in self-similarity (and its generalizations, fusions rules and S-adic systems), algebraic developments connected to physics, games and undecidability questions, and the spectrum of substitution tilings. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2273 606 $aTiling (Mathematics) 606 $aSequences (Mathematics) 615 0$aTiling (Mathematics) 615 0$aSequences (Mathematics) 676 $a511.5 702 $aAkiyama$b Shigeki 702 $aArnoux$b P$g(Pierre), 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bUtOrBLW 906 $aBOOK 912 $a996418192803316 996 $aSubstitution and tiling dynamics$92087478 997 $aUNISA