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数学专著丛书:平面动力系统的若干经典问题(英文版)
浅水波,非线性光学、电磁学、等离子物理、凝聚态物理、生物及化学、通讯等领域均存在非线性波运动。对其数学模型--波方程的解研究有重要价值。上世纪90年代,数学家发现了行波方程的非光滑的孤粒子解(peakon)、有限支集解(compacton)和圈解(loopsolution)等,为理解这些解,特别是非光滑解的出现,导致用动力系统的分支理论及方法对奇行波方程进行研究的新方向。《数学专著丛书:平面动力系统的若干经典问题(英文版)》介绍两类奇行波方程的研究的动力系统方法,及对大量数学物理问题的应用。
theComputAtionofSingulArPointVAlues782.4TheAlgebrAicConstructionofSingulArVAlues.832.5ElementAryGenerAlizedRotAtionInvAriAntsoftheCubicSystems882.6SingulArPointVAluesAndIntegrAbilityConditionoftheQuAdrAticSystems.902.7SingulArPointVAluesAndIntegrAbilityConditionoftheCubicSystemsHAvingHomogeneousNonlineArities933MultipleHopfBifurcAtions973.1TheZerosofSuccessorFunctionsinthePolArCoordinAtes973.2AnAlyticEquivAlence.100QuAsiSuccessorFunction1023.33.4BifurcAtionsofLimitCircleofAClAssofQuAdrAticSystems.1084IsochronousCenterInComplexDomAin.1114.1IsochronousCentersAndPeriodConstAnts.111xiiContents4.2LineArRecursiveFormulAstoComputePeriodConstAnts1164.3IsochronousCenterforAClAssofQuinticSystemintheComplexDomAin.122.1234.3.1TheConditionsofIsochronousCenterUnderConditionC1.1244.3.2TheConditionsofIsochronousCenterUnderConditionC2.1274.3.3TheConditionsofIsochronousCenterUnderConditionC31284.3.4Non-IsochronousCenterunderConditionC4AndC4.4.4TheMethodofTime-AngleDi.erence1284.5TheConditionsofIsochronousCenteroftheOriginforACubicSystem.1345TheoryofCenter-FocusAndBifurcAtionofLimitCyclesAtIn.nityofAClAssofSystems1385.1De.nitionoftheFocAlVAluesofIn.nity138ConversionofQuestions.1415.25.3MethodofFormAlSeriesAndSingulArPointVAlueofIn.nity.1445.4TheAlgebrAicConstructionofSingulArPointVAluesofIn.nity.1565.5SingulArPointVAluesAtIn.nityAndIntegrAbleConditionsforAClAssofCubicSystem.1615.6BifurcAtionofLimitCyclesAtIn.nity1685.7IsochronousCentersAtIn.nityofAPolynomiAlSystems1725.7.1ConditionsofComplexCenterforSystem(5.7.6).1735.7.2ConditionsofComplexIsochronousCenterforSystem(5.7.6)1766TheoryofCenter-FocusAndBifurcAtionsofLimitCyclesforAClAssofMultipleSingulArPoints.1806.1SuccessionFunctionAndFocAlVAluesforAClAssofMultipleSingulArPoints.180ConversionoftheQuestions1826.26.3FormAlSeries,IntegrAlFActorsAndSingulArPointVAluesforAClAssofMultipleSingulArPoints1846.4TheAlgebrAicStructureofSingulArPointVAluesofAClAssofMultipleSingulArPoints.1966.5BifurcAtionofLimitCyclesFromAClAssofMultipleSingulArPoints.1986.6BifurcAtionofLimitCyclesCreAtedfromAMultipleSingulArPointforAClAssofQuArticSystem1996.7QuAsiIsochronousCenterofMultipleSingulArPointforContentsxiiiAClAssofAnAlyticSystem.2027OnQuAsiAnAlyticSystems.2057.1PreliminAry205ReductionoftheProblems2087.27.3FocAlVAlues,PeriodicConstAntsAndFirstIntegrAlsof(7.2.3)2107.4SingulArPointVAluesAndBifurcAtionsofLimitCyclesofQuAsi-QuAdrAticSystems2147.5IntegrAbilityofQuAsi-QuAdrAticSystems2177.6IsochronousCenterofQuAsi-QuAdrAticSystems2197.6.1TheProblemofComplexIsochronousCentersUnder.219theConditionofC17.6.2TheProblemofComplexIsochronousCentersUnder.222theConditionofC27.6.3TheProblemofComplexIsochronousCentersUndertheOtherConditions2257.7SingulArPointVAluesAndCenterConditionsforAClAssofQuAsi-CubicSystems2288LocAlAndNon-LocAlBifurcAtionsofPerturbedZq-EquivAriAntHAmiltoniAnVectorFields2328.1Zq-EquivAriAntPlAnArVectorFieldsAndAnExAmple2328.2TheMethodofDetectionFunctions:RoughPerturbAtionsofZq-EquivAriAntHAmiltoniAnVectorFields.2428.3BifurcAtionsofLimitCyclesofAZ2-EquivAriAntPerturbedHAmiltoniAnVectorFields2448.3.1HopfBifurcAtionPArAmeterVAlues2468.3.2BifurcAtionsFromHeteroclinicorHomoclinicLoops.2478.3.3TheVAluesofBifurcAtionDirectionsofHeteroclinicAndHomoclinicLoops2528.3.4AnAlysisAndConclusions2558.4TheRAteofGrowthofHilbertNumberH(n)withn2588.4.1PreliminAryLemmAs2598.4.2ACorrectiontotheLowerBoundsofH(2k.1)Givenin[ChristopherAndLloyd,1995]2628.4.3ANewLowerBoundforH(2k.1)2658.4.4LowerBoundforH(3×2k.1.1)2679Center-FocusProblemAndBifurcAtionsofLimitCyclesxivContentsforAZ2-EquivAriAntCubicSystem.2729.1StAndArdFormofAClAssofSystem(EZ2).27239.2LiApunovConstAnts,InvAriAntIntegrAlsAndtheNecessAryAndSu.cientConditionsoftheExistencefortheBi-Center.2749.3TheConditionsofSix-OrderWeAkFocusAndBifurcAtionsofLimitCycles.2869.4AClAssof(EZ2)SystemWith13LimitCycles2903ProofsofLemmA9.4.1AndTheorem9.4.1.2949.59.6TheProofsofLemmA9.4.2AndLemmA9.4.3.30010Center-FocusProblemAndBifurcAtionsofLimitCyclesforThree-MultipleNilpotentSingulArPoints30810.1CriteriAofCenter-FocusforANilpotentSingulArPoint30810.2SuccessorFunctionsAndFocusVAlueofThree-MultipleNilpotentSingulArPoint31110.3BifurcAtionofLimitCyclesCreAtedfromThree-MultipleNilpotentSingulArPoint31410.4TheClAssi.cAtionofThree-MultipleNilpotentSingulArPointsAndInverseIntegrAlFActor32110.5QuAsi-LyApunovConstAntsFortheThree-MultipleNilpotentSingulArPoint326ProofofTheorem10.5.232910.610.7OntheComputAtionofQuAsi-LyApunovConstAnts.33310.8BifurcAtionsofLimitCyclesCreAtedfromAThree-MultipleNilpotentSingulArPointofACubicSystem336BibliogrAphy.341Index368
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