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1、LectureNotesinMathematicsEditedbyA.DoldandB.EckmannSeries:AustralianNationalUniversity,CanberraAdviser:M.F.Newman629W.A.CoppelDichotomiesinStabilityTheorySpringer-VerlagBerlinHeidelbergNewYork1978AuthorW.A.CoppelDepartmentofMathematicsInstituteofAdvancedStudiesAustralian
2、NationalUniversityCanberra,ACT,2600/AustraliaAMSSubjectClassifications(1970):34D05,58F15ISBN3-540-08536-XSpringer-VerlagBerlinHeidelbergNewYorkISBN0-387-08536-XSpringer-VerlagNewYorkHeidelbergBerlinThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartof
3、thematerialisconcerned,specificallythoseoftranslation,re-printing,re-useofillustrations,broadcasting,reproductionbyphotocopyingmachineorsimilarmeans,andstorageindatabanks.Under§54oftheGermanCopyrightLawwherecopiesaremadeforotherthanprivateuse,afeeispayabletothepublisher,
4、theamountofthefeetobedeterminedbyagreementwiththepublisher.©bySpringer-VerlagBerlinHeidelberg1978PrintedinGermanyPrintingandbinding:BeltzOffsetdruck,Hemsbach/Bergstr.2140/3140-543210PREFACESeveralyearsagoIformedtheviewthatdichotomies,ratherthanLyapunov'scharacteristicexp
5、onents,arethekeytoquestionsofasymptoticbehaviourfornon-autonomousdifferentialequations.Istillholdthatview,inspiteofthefactthatsincethentherehaveappearedmanymorepapersandabookoncharacteristicexponents.Ontheotherhand,therehasrecentlybeenanimportantnewdevelopmentinthetheory
6、ofdichotomies.Thusitseemedtomeanappropriatetimetogiveanaccessibleaccountofthisattractivetheory.ThepresentlecturenotesarethebasisforacoursegivenattheUniversityofFlorenceinMay,1977.IamgratefultoProfessorR.Contifortheinvitationtovisitthereandforprovidingtheincentivetoputmyt
7、houghtsinorder.IamalsogratefultoMrsHelenDaishandMrsLindaSouthwellforcheerfullyandcarefullytypingthemanuscript.CONTENTSLectureI.STABILITY................................................Lecture2.EXPONENTIALANDORDINARYDICHOTOMIES.....................i0Lecture3.DICHOTOMIESAN
8、DFUNCTIONALANALYSIS......................20Lecture4.ROUGHNESS..........................................
