无处不在的分形（第2版）

图书标准信息

• 作者 [英]巴恩斯利（Barnsley M.F） 著
• 出版社 世界图书出版公司
• 出版时间 2009-01
• 版次 1
• ISBN 9787506292733
• 定价 96.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 531页
• 正文语种 英语

【内容简介】

　　Iacknowledgeandthankmanypeoplefortheirhelpwiththisbook.InparticularIthankAlanSloan，whohasunceasinglyencouragedme，whowrotethefirstCollagesoftware，andwhosoclearlyenvisionedtheapplicationofiteratedfunctionsystemstoimagecompressionandcommunicationsthathefoundedacompanynamedIteratedSystemsIncorporated.EdwardVrscay，whotaughtthefirstcourseindeterministicfractalgeometryatGeorgiaTech，sharedhisideasabouthowthecoursecouldbetaught，andsuggestedsomesubjectsforinclusioninthistext.StevenDemko，whocollaboratedwithmeonthediscoveryofiteratedfunctionsystems，madeearlydetailedproposalsonhowthesubjectcouldbepresentedtostudentsandscientists，andprovidedcommentsonseveralchapters.AndrewHarringtonandJeffreyGeronimo，whodiscoveredwithmeorthogonalpolynomialsonJuliasets.Mycollaborationswiththemoverfiveyearsformedformethefoundationonwhichiteratedfunctionsystemsarebuilt.Watchformorepapersfromus！
　　LesKarlovitz，whoencouragedandsupportedmyresearchoverthelastnineyears，obtainedthetimeformetowritethisbookandprovidedspecifichelp，advice，anddirection.Hiswordscanbefoundinsomeofthesentencesinthetext.GunterMeyer，whohasencouragedandsupportedmyresearchoverthelastnineyears.Hehasoftengivenmegoodadvice.RobertKasriel，whotaughtmesometopologyoverthelasttwoyears，correctedandrewrotemyproofofTheorem7.1inChapterIIandcontributedotherhelpandwarmencouragement.NathanialChafee，whoreadandcorrectedChapterIIandearlydraftsofChaptersIIIandIV.Hisaptconstructivecommentshaveincreasedsubstantiallytheprecisionofthewriting.JohnElton，whotaughtmesomeergodictheory，continuestocollaborateonexcitingresearchintoiteratedfunctionsystems，andhelpedmewithmanypartsofthebook.DanielBessisandPierreMoussa，whoarefilledwiththewonderandmysteryofscience，andtaughtmetolookformathematicaleventsthataresoastonishingthattheymaybecalledmiracles.ResearchworkwithBessisandMoussaatSaclayduring1978，ontheDiophantineMomentProblemandIsingModels，wastheseedthatgrewintothisbook.WarrenStahle，whoprovidedsomeofhisexperimentalresearchresults.

【目录】

Foreword
Acknowledgments
ChapterIIntroduction
ChapterIIMetricSpaces;EquivalentSpaces;ClassificationofSubsets;andtheSpaceofFractals
1.Spaces
2.MetricSpaces
3.CauchySequences，LimitPoints，ClosedSets，PerfectSets，andCompleteMetricSpaces
4.CompactSets，BoundedSets，OpenSets，Interiors，andBoundaries
5.ConnectedSets，DisconnectedSets，andPathwiseConnectedSets
6.TheMetricSpace(H(X)，h)：ThePlaceWhereFractalsLive
7.TheCompletenessoftheSpaceofFractals
8.AdditionalTheoremsaboutMetricSpaces

ChapterIIITransformationsonMetricSpaces;ContractionMapplngs;andtheConstructionofFractals
1.TransformationsontheRealLine
2.AffineTransformationsintheEuclideanPlane
3.MObiusTransformationsontheRiemannSphere
4.AnalyticTransformations
5.HowtoChangeCoordinates
6.TheContractionMappingTheorem
7.ContractionMappingsontheSpaceofFractals
8.TwoAlgorithmsforComputingFractalsfromIteratedFunctionSystems
9.CondensationSets
10.HowtoMakeFractalModelswiththeHelpoftheCollageTheorem
11.BlowingintheWind：TheContinousDependenceofFractalsonParameters

ChapterIVChaoticDynamicsonFractal$
1.TheAddressesofPointsonFractals
2.ContinuousTransformationsfromCodeSpacetoFractals
3.IntroductiontoDynamicalSystems
4.DynamicsonFractals：OrHowtoComputeOrbitsbyLookingatPictures
5.EquivalentDynamicalSystems
6.TheShadowofDeterministicDynamics
7.TheMeaningfulnessofInaccuratelyComputedOrbitsisEstablishedbyMeansofaShadowingTheorem
8.ChaoticDynamicsonFractals

ChapterVFractalDimension
1.FractalDimension
2.TheTheoreticalDeterminationoftheFractalDimension
3.TheExperimentalDeterminationoftheFractalDimension
4.TheHausdorff-BesicovitchDimension

ChapterVlFractalInterpolation
1.Introduction：ApplicationsforFractalFunctions
2.FractalInterpolationFunctions
3.TheFractalDimensionofFractalInterpolationFunctions
4.HiddenVariableFractalInterpolation
5.Space-FillingCurves

ChapterVIIJullaSets
1.TheEscapeTimeAlgorithmforComputingPicturesofIFSAttractorsandJuliaSets
2.IteratedFunctionSystemsWhoseAttractorsAreJuliaSets
3.TheApplicationofJuliaSetTheorytoNewtonsMethod
4.ARichSourceforFractals：InvariantSetsofContinuousOpenMappings

ChapterVIIIParameterSpacesandMandelbrotSets
1.TheIdeaofaParameterSpace：AMapofFractals
2.MandelbrotSetsforPairsofTransformations
3.TheMandelbrotSetforJuliaSets
4.HowtoMakeMapsofFamiliesofFractalsUsingEscapeTimes

ChapterIXMeasuresonFractals
1.IntroductiontoInvariantMeasuresonFractals
2.FieldsandSigma-Fields
3.Measures
4.Integration
5.TheCompactMetricSpace(P(X)，d)
6.AContractionMappingon(~~o(X))
7.EltonsTheorem
8.ApplicationtoComputerGraphics

ChapterXRecurrentIteratedFunctionSystems
1.FractalSystems
2.RecurrentIteratedFunctionSystems
3.CollageTheoremforRecurrentIteratedFunctionSystems
4.FractalSystemswithVectorsofMeasuresasTheirAttractors
5.References
References
SelectedAnswers
Index
CredltsforFiguresandColorPlates