LEADER 05155nam 22008775 450 001 9910144941103321 005 20200704164411.0 010 $a3-540-45714-3 024 7 $a10.1007/b13861 035 $a(CKB)1000000000233280 035 $a(SSID)ssj0000327011 035 $a(PQKBManifestationID)11263389 035 $a(PQKBTitleCode)TC0000327011 035 $a(PQKBWorkID)10299173 035 $a(PQKB)10204655 035 $a(DE-He213)978-3-540-45714-5 035 $a(MiAaPQ)EBC3071819 035 $a(PPN)155182153 035 $a(EXLCZ)991000000000233280 100 $a20121227d2002 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aSubstitutions in Dynamics, Arithmetics and Combinatorics /$fby N. Pytheas Fogg ; edited by Valerie Berthé, Sebastien Ferenczi, Christian Mauduit, Anne Siegel 205 $a1st ed. 2002. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2002. 215 $a1 online resource (XX, 404 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1794 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-44141-7 320 $aIncludes bibliographical references and index. 327 $aBasic notions on substitutions -- Basic notions on substitutions -- Arithmetics and combinatorics of substitutions -- Substitutions, arithmetic and finite automata: an introduction -- Automatic sequences and transcendence -- Substitutions and partitions of the set of positive integers -- Dynamics of substitutions -- Substitutions and symbolic dynamical systems -- Sturmian Sequences -- Spectral theory and geometric representation of substitutions -- Diophantine approximations, substitutions, and fractals -- Extensions to free groups and interval transformations -- Infinite words generated by invertible substitutions -- Polynomial dynamical systems associated with substitutions -- Piecewise linear transformations of the unit interval and Cantor sets -- Some open problems -- A. Undecomposable matrices in dimension 3 (by J. Rivat). 330 $aA certain category of infinite strings of letters on a finite alphabet is presented here, chosen among the 'simplest' possible one may build, both because they are very deterministic and because they are built by simple rules (a letter is replaced by a word, a sequence is produced by iteration). These substitutive sequences have a surprisingly rich structure. The authors describe the concepts of quantity of natural interactions, with combinatorics on words, ergodic theory, linear algebra, spectral theory, geometry of tilings, theoretical computer science, diophantine approximation, trancendence, graph theory. This volume fulfils the need for a reference on the basic definitions and theorems, as well as for a state-of-the-art survey of the more difficult and unsolved problems. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1794 606 $aNumber theory 606 $aFunctions of real variables 606 $aDynamics 606 $aErgodic theory 606 $aSequences (Mathematics) 606 $aComputers 606 $aLogic, Symbolic and mathematical 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 606 $aReal Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12171 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aSequences, Series, Summability$3https://scigraph.springernature.com/ontologies/product-market-codes/M1218X 606 $aComputation by Abstract Devices$3https://scigraph.springernature.com/ontologies/product-market-codes/I16013 606 $aMathematical Logic and Formal Languages$3https://scigraph.springernature.com/ontologies/product-market-codes/I16048 615 0$aNumber theory. 615 0$aFunctions of real variables. 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aSequences (Mathematics) 615 0$aComputers. 615 0$aLogic, Symbolic and mathematical. 615 14$aNumber Theory. 615 24$aReal Functions. 615 24$aDynamical Systems and Ergodic Theory. 615 24$aSequences, Series, Summability. 615 24$aComputation by Abstract Devices. 615 24$aMathematical Logic and Formal Languages. 676 $a510 s 676 $a511.3 700 $aPytheas Fogg$b N$4aut$4http://id.loc.gov/vocabulary/relators/aut$0352583 702 $aBerthé$b Valerie$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aFerenczi$b Sebastien$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aMauduit$b Christian$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aSiegel$b Anne$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910144941103321 996 $aSubstitutions in dynamics, arithmetics and combinatorics$91432028 997 $aUNINA