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1、SpringerMonographsinMathematicsTomyRiemannzeros:Odile,JulieandMicha¨el,mymuseandoffspringMichelL.LapidusToJena,DavidandSamuelMachielvanFrankenhuijsenMichelL.LapidusMachielvanFrankenhuijsenFractalGeometry,ComplexDimensionsandZetaFunctionsGeometryandSpectraofFractalStringsWith53IllustrationsMiche
2、lL.LapidusMachielvanFrankenhuijsenUniversityofCaliforniaUtahValleyStateCollegeDepartmentofMathematicsDepartmentofMathematics231SurgeBuilding800WestUniversityParkwayRiverside,CA92521-0135Orem,Utah84058-5999USAUSAlapidus@math.ucr.eduvanframa@uvsc.eduThefrontcovershowsatubularneighborhoodoftheDev
3、il’sstaircase(Figure12.2,page335)andthequasiperiodicpatternofthecomplexdimensionsofanonlatticeself-similarstring(Figure3.7,page86).MathematicsSubjectClassification(2000):Primary–11M26,11M41,28A75,28A80,35P20,58G25Secondary–11J70,11M06,11N05,28A12,30D35,81Q20LibraryofCongressControlNumber:20069
4、29212ISBN-10:0-387-33285-5e-ISBN:0-387-35208-2ISBN-13:978-0-387-33285-7Printedonacid-freepaper.©2006SpringerScience+BusinessMedia,LLCAllrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMedia,LLC,233SpringStreet,Ne
5、wYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,tra
6、demarks,servicemarks,andsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.PrintedintheUnitedStatesofAmerica.(EB)987654321springer.comContentsPrefacexiListofFiguresxvListofTablesxixOverviewxxiIntroduction11Comple
7、xDimensionsofOrdinaryFractalStrings91.1TheGeometryofaFractalString...............91.1.1TheMultiplicityoftheLengths............121.1.2Example:TheCantorString.............131.2TheGeometricZetaFunctionofaFractalString......161.2.1TheScreen
