000 04407nam a22006135i 4500
001 978-3-540-45714-5
003 DE-He213
005 20190213151549.0
007 cr nn 008mamaa
008 121227s2002 gw | s |||| 0|eng d
020 _a9783540457145
_9978-3-540-45714-5
024 7 _a10.1007/b13861
_2doi
050 4 _aQA241-247.5
072 7 _aPBH
_2bicssc
072 7 _aMAT022000
_2bisacsh
072 7 _aPBH
_2thema
082 0 4 _a512.7
_223
245 1 0 _aSubstitutions in Dynamics, Arithmetics and Combinatorics
_h[electronic resource] /
_cedited by N. Pytheas Fogg, Valéré Berthé, Sébastien Ferenczi, Christian Mauduit, Anne Siegel.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2002.
300 _aXX, 404 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1794
505 0 _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).
520 _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.
650 0 _aNumber theory.
650 0 _aMathematics.
650 0 _aDifferentiable dynamical systems.
650 0 _aSequences (Mathematics).
650 0 _aComputer science.
650 1 4 _aNumber Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M25001
650 2 4 _aReal Functions.
_0http://scigraph.springernature.com/things/product-market-codes/M12171
650 2 4 _aDynamical Systems and Ergodic Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M1204X
650 2 4 _aSequences, Series, Summability.
_0http://scigraph.springernature.com/things/product-market-codes/M1218X
650 2 4 _aComputation by Abstract Devices.
_0http://scigraph.springernature.com/things/product-market-codes/I16013
650 2 4 _aMathematical Logic and Formal Languages.
_0http://scigraph.springernature.com/things/product-market-codes/I16048
700 1 _aFogg, N. Pytheas.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
700 1 _aBerthé, Valéré.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
700 1 _aFerenczi, Sébastien.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
700 1 _aMauduit, Christian.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
700 1 _aSiegel, Anne.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662212264
776 0 8 _iPrinted edition:
_z9783540441410
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1794
856 4 0 _uhttps://doi.org/10.1007/b13861
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c11111
_d11111