000 03207nam a22004575i 4500
001 978-3-642-14034-1
003 DE-He213
005 20140220084540.0
007 cr nn 008mamaa
008 100825s2010 gw | s |||| 0|eng d
020 _a9783642140341
_9978-3-642-14034-1
024 7 _a10.1007/978-3-642-14034-1
_2doi
050 4 _aQA313
072 7 _aPBWR
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515.39
_223
082 0 4 _a515.48
_223
100 1 _aCeccherini-Silberstein, Tullio.
_eauthor.
245 1 0 _aCellular Automata and Groups
_h[electronic resource] /
_cby Tullio Ceccherini-Silberstein, Michel Coornaert.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2010.
300 _aXX, 440 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Monographs in Mathematics,
_x1439-7382
505 0 _aCellular Automata -- Residually Finite Groups -- Surjunctive Groups -- Amenable Groups -- The Garden of Eden Theorem -- Finitely Generated Amenable Groups -- Local Embeddability and Sofic Groups -- Linear Cellular Automata -- Nets and the Tychonoff Product Theorem -- Uniform Structures -- Symmetric Groups -- Free Groups -- Inductive Limits and Projective Limits of Groups -- The Banach-Alaoglu Theorem -- The Markov-Kakutani Fixed Point Theorem -- The Hall Harem Theorem -- Complements of Functional Analysis -- Ultrafilters.
520 _aCellular automata were introduced in the first half of the last century by John von Neumann who used them as theoretical models for self-reproducing machines. The authors present a self-contained exposition of the theory of cellular automata on groups and explore its deep connections with recent developments in geometric group theory, symbolic dynamics, and other branches of mathematics and theoretical computer science. The topics treated include in particular the Garden of Eden theorem for amenable groups, and the Gromov-Weiss surjunctivity theorem as well as the solution of the Kaplansky conjecture on the stable finiteness of group rings for sofic groups. The volume is entirely self-contained, with 10 appendices and more than 300 exercises, and appeals to a large audience including specialists as well as newcomers in the field. It provides a comprehensive account of recent progress in the theory of cellular automata based on the interplay between amenability, geometric and combinatorial group theory, symbolic dynamics and the algebraic theory of group rings which are treated here for the first time in book form.
650 0 _aMathematics.
650 0 _aDifferentiable dynamical systems.
650 1 4 _aMathematics.
650 2 4 _aDynamical Systems and Ergodic Theory.
700 1 _aCoornaert, Michel.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642140334
830 0 _aSpringer Monographs in Mathematics,
_x1439-7382
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-14034-1
912 _aZDB-2-SMA
999 _c112391
_d112391