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1、SpringerMonographsinMathematicsForfurthervolumes:www.springer.com/series/3733TullioCeccherini-SilbersteinMichelCoornaertCellularAutomataandGroupsTullioCeccherini-SilbersteinMichelCoornaertDipartimentodiIngegneriaInstitutdeRechercheMathématiqueAvancé
2、eUniversitàdelSannioUniversitédeStrasbourgC.soGaribaldi1077rueRené-Descartes82100Benevento67084StrasbourgCedexItalyFrancetceccher@mat.uniroma1.itcoornaert@math.unistra.frISSN1439-7382ISBN978-3-642-14033-4e-ISBN978-3-642-14034-1DOI10.1007/978-3-642-14
3、034-1SpringerHeidelbergDordrechtLondonNewYorkLibraryofCongressControlNumber:2010934641MathematicsSubjectClassification(2010):37B15,68Q80,20F65,43A07,16S34,20C07©Springer-VerlagBerlinHeidelberg2010Thisworkissubjecttocopyright.Allrightsarereserved,wheth
4、erthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublicationorpartsthereofispermittedonlyun
5、dertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.ViolationsareliabletoprosecutionundertheGermanCopyrightLaw.Theuseofgeneraldescriptivenames,registerednames,trademarks,etc
6、.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.Coverdesign:deblikPrintedonacid-freepaperSpringerispartofSpringerScience+BusinessMedia(w
7、ww.springer.com)ToKatiuscia,Giacomo,andTommasoToMartineandNathaliePrefaceTwoseeminglyunrelatedmathematicalnotions,namelythatofanamenablegroupandthatofacellularautomaton,werebothintroducedbyJohnvonNeumanninthefirsthalfofthelastcentury.Amenability,which
8、originatedfromthestudyoftheBanach-Tarskiparadox,isapropertyofgroupsgener-alizingbothcommutativityandfiniteness.Nowadays,itplaysanimportantroleinmanyareasofmathematicssuchasrepresentationtheory,harmonicanalysis,ergodictheory,geometricgrouptheory,probab
