05153nam 22008775 450 99646661750331620200704164411.03-540-45714-310.1007/b13861(CKB)1000000000233280(SSID)ssj0000327011(PQKBManifestationID)11263389(PQKBTitleCode)TC0000327011(PQKBWorkID)10299173(PQKB)10204655(DE-He213)978-3-540-45714-5(MiAaPQ)EBC3071819(PPN)155182153(EXLCZ)99100000000023328020121227d2002 u| 0engurnn|008mamaatxtccrSubstitutions in Dynamics, Arithmetics and Combinatorics[electronic resource] /by N. Pytheas Fogg ; edited by Valerie Berthé, Sebastien Ferenczi, Christian Mauduit, Anne Siegel1st ed. 2002.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2002.1 online resource (XX, 404 p.) Lecture Notes in Mathematics,0075-8434 ;1794Bibliographic Level Mode of Issuance: Monograph3-540-44141-7 Includes bibliographical references and index.Basic 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).A 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.Lecture Notes in Mathematics,0075-8434 ;1794Number theoryFunctions of real variablesDynamicsErgodic theorySequences (Mathematics)ComputersMathematical logicNumber Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M25001Real Functionshttps://scigraph.springernature.com/ontologies/product-market-codes/M12171Dynamical Systems and Ergodic Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M1204XSequences, Series, Summabilityhttps://scigraph.springernature.com/ontologies/product-market-codes/M1218XComputation by Abstract Deviceshttps://scigraph.springernature.com/ontologies/product-market-codes/I16013Mathematical Logic and Formal Languageshttps://scigraph.springernature.com/ontologies/product-market-codes/I16048Number theory.Functions of real variables.Dynamics.Ergodic theory.Sequences (Mathematics).Computers.Mathematical logic.Number Theory.Real Functions.Dynamical Systems and Ergodic Theory.Sequences, Series, Summability.Computation by Abstract Devices.Mathematical Logic and Formal Languages.510 s511.3Pytheas Fogg Nauthttp://id.loc.gov/vocabulary/relators/aut352583Berthé Valerieedthttp://id.loc.gov/vocabulary/relators/edtFerenczi Sebastienedthttp://id.loc.gov/vocabulary/relators/edtMauduit Christianedthttp://id.loc.gov/vocabulary/relators/edtSiegel Anneedthttp://id.loc.gov/vocabulary/relators/edtMiAaPQMiAaPQMiAaPQBOOK996466617503316Substitutions in dynamics, arithmetics and combinatorics1432028UNISA