Springer.Local.and.semi.local.bifurcations.in.hamiltonian.dynamical.systems.results.and.examples.(LNM.1893.Springer.2007)(ISBN.354038894X)(247s)

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1、LectureNotesinMathematics1893Editors:J.-M.Morel,CachanF.Takens,GroningenB.Teissier,ParisHeinzHanßmannLocalandSemi-LocalBifurcationsinHamiltonianDynamicalSystemsResultsandExamplesABCAuthorHeinzHanßmannMathematischInstituutUniversiteitUtrechtPostbus800103508TAUtrechtTheNet

2、herlandsLibraryofCongressControlNumber:2006931766MathematicsSubjectClassification(2000):37J20,37J40,34C30,34D30,37C15,37G05,37G10,37J15,37J35,58K05,58K70,70E20,70H08,70H33,70K30,70K43ISSNprintedition:0075-8434ISSNelectronicedition:1617-9692ISBN-103-540-38894-xSpringerBerl

3、inHeidelbergNewYorkISBN-13978-3-540-38894-4SpringerBerlinHeidelbergNewYorkDOI10.1007/3-540-38894-xThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,

4、broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.DuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violations

5、areliableforprosecutionundertheGermanCopyrightLaw.SpringerisapartofSpringerScience+BusinessMediaspringer.com°cSpringer-VerlagBerlinHeidelberg2007Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstateme

6、nt,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.TypesettingbytheauthorandSPiusingaSpringerLATEXpackageCoverdesign:WMXDesignGmbH,HeidelbergPrintedonacid-freepaperSPIN:11841708VA41/3100/SPi543210tomyparentsPrefaceLifeisinco

7、lor,Butblackandwhiteismorerealistic.SamuelFullerThepresentnotesaredevotedtothestudyofbifurcationsofinvarianttoriinHamiltoniansystems.Hamiltoniandynamicalsystemscanbeusedtomodelfrictionlessmechanics,inparticularcelestialmechanics.Weareconcernedwiththenearlyintegrableconte

8、xt,whereKolmogorov–Arnol’d–Moser(KAM)theoryshowsthatmostmotionsarequasi-periodicwhencethe(invariant)clo