dynamics in infinite dimensions (jack k hale)

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1、DynamicsinInfiniteDimensions,SecondEditionJackK.HaleLuisT.MagalhãesWaldyrM.OlivaSpringerPrefaceInourbookpublishedin1984AnIntroductiontoInfiniteDimensionalDy-namicalSystems-GeometricTheory,wepresentedsomeaspectsofageomet-rictheoryofinfinitedimensionalspaceswi

2、thmajoremphasisonretardedfunctionaldifferentialequations.Inthisbook,theintentisthesame.TherearenewresultsonMorse–Smalesystemsforsemiflows,persistenceofhyper-bolicityunderperturbations,nonuniformhyperbolicity,monotonedynamicalsystems,realizationofvectorfieldso

3、ncentermanifoldsandnormalforms.Inaddition,moreattentionisdevotedtoneutralfunctionaldifferentialequa-tionsalthoughthetheoryismuchlessdeveloped.Somepartsofthetheoryalsowillapplytomanyothertypesofequationsandapplications.JackK.HaleLuisT.Magalh˜aesWaldyrM.Oliva

4、ThispageintentionallyleftblankContentsPreface.......................................................v1Introduction..............................................12InvariantSetsandAttractors.............................73FunctionalDifferentialEquationsonManif

5、olds...........193.1RFDEonmanifolds....................................193.2ExamplesofRFDEonmanifolds.........................293.3NFDEonmanifolds....................................443.4NFDEonRn..........................................463.4.1Generalprope

6、rties................................463.4.2Equivalenceofpointandcompactdissipative........503.5AnexampleofNFDEonS1.............................523.6AcanonicalODEintheFr´echetcategory..................544TheDimensionoftheAttractor..........................

7、575StabilityandBifurcation.................................656StabilityofMorse–SmaleMapsandSemiflows............816.1Morse–Smalemaps.....................................816.2Morse–Smalesemiflows..................................986.3Anexample................

8、............................1047One-to-Oneness,Persistence,andHyperbolicity..........1097.1ThesemiflowofanRFDEonacompactmanifoldM........1107.2Hyperbolicinvariantsets................................1117.3Hyper