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[美] 米尔诺 (John Milnor) 著 / 世界图书出版公司 / 2013-03 / 平装
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ThisbookstudiesthedynamicsofiteratedholomorphicmappingsfromaRiemannsurfacetoitself,concentratingontheclassicalcaseofrational.mapsoftheRiemannsphere.ItisbasedonintroductorylecturesgivenatStonyBrookduringthefalltermof1989-90andinlateryears.IamgratefultotheaudiencesforagreatdealofconstructivecriticismandtoBodilBranner,AdrienDouady,JohnHubbard,andMitsuhiroShishikura,whotaughtmemostofwhatIknowinthisfield.Also,Iwanttothankanumberofindividualsfortheirextremelyhelpfulcriticismsandsuggestions,especiallyAdamEpstein,RodrigoPerez,AlfredoPoirier,LasseRempe,andSaeedZakeri.AraceliBonifanthasbeenparticularlyhelpfulinthepreparationofthisthirdedition.
ListofFiguresPrefacetotheThirdEditionChronologicalTableRiemannSurfaces1.SimplyConnectedSurfaces2.UniversalCoveringsandthePoincareMetric3.NormalFamilies:Montel'sTheoremIteratedHolomorphicMaps4.FatouandJulia:DynamicsontheRiemannSphere5.DynamicsonHyperbolicSurfaces6.DynamicsonEuclideanSurfaces7.SmoothJuliaSetsLocalFixedPointTheory8.GeometricallyAttractingorRepellingFixedPoints9.Bottcher'sTheoremandPolynomialDynamics10.ParabolicFixedPoints:TheLeau-FatouFlower11.CremerPointsandSiegelDisksPeriodicPoints:GlobalTheory12.TheHolomorphicFixedPointFormula13.MostPeriodicOrbitsRepel14.RepellingCyclesAreDenseinJStructureoftheFatouSet15.HermanRings16.TheSullivanClassificationofFatouComponentsUsingtheFatouSettoStudytheJuliaSet17.PrimeEndsandLocalConnectivity18.PolynomialDynamics:ExternalRays19.HyperbolicandSubhyperbolicMapsAppendixA.TheoremsfromClassicalAnalysisAppendixB.Length-Area-ModulusInequalitiesAppendixC.Rotations,ContinuedFractions,andRationalApproximationAppendixD.TwoorMoreComplexVariablesAppendixE.BranchedCoveringsandOrbifoldsAppendixF.NoWanderingFatouComponentsAppendixG.ParameterSpacesAppendixH.ComputerGraphicsandEffectiveComputationReferencesIndex
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