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1、SpringerMonographsinMathematicsTomyRiemannzeros:Odile,JulieandMicha¨el,mymuseandoffspringMichelL.LapidusToJena,DavidandSamuelMachielvanFrankenhuijsenMichelL.LapidusMachielvanFrankenhuijsenFractalGeometry,ComplexDimensionsandZetaFunctionsGeometryandSpect
2、raofFractalStringsWith53IllustrationsMichelL.LapidusMachielvanFrankenhuijsenUniversityofCaliforniaUtahValleyStateCollegeDepartmentofMathematicsDepartmentofMathematics231SurgeBuilding800WestUniversityParkwayRiverside,CA92521-0135Orem,Utah84058-5999USAUS
3、Alapidus@math.ucr.eduvanframa@uvsc.eduThefrontcovershowsatubularneighborhoodoftheDevil’sstaircase(Figure12.2,page335)andthequasiperiodicpatternofthecomplexdimensionsofanonlatticeself-similarstring(Figure3.7,page86).MathematicsSubjectClassification(2000
4、):Primary–11M26,11M41,28A75,28A80,35P20,58G25Secondary–11J70,11M06,11N05,28A12,30D35,81Q20LibraryofCongressControlNumber:2006929212ISBN-10:0-387-33285-5e-ISBN:0-387-35208-2ISBN-13:978-0-387-33285-7Printedonacid-freepaper.©2006SpringerScience+BusinessMe
5、dia,LLCAllrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMedia,LLC,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.
6、Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveni
7、ftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.PrintedintheUnitedStatesofAmerica.(EB)987654321springer.comContentsPrefacexiListofFiguresxvListofTablesxixOverviewxxiIntroduction11Comple
8、xDimensionsofOrdinaryFractalStrings91.1TheGeometryofaFractalString...............91.1.1TheMultiplicityoftheLengths............121.1.2Example:TheCantorString.............131.2TheGeometricZetaFunctionofaFractalString......161.2.1TheScreen
