二阶非线性系统的奇点量、中心问题与极限环分叉

Chapter1FocalValues,SaddleValuesandSingularPointValues

1.1SuccessorFunctionsandPropertiesofFocalValues

1.2PoincareFormalSeriesandAlgebraicEquivalence

1.3SingularPointValuesandConditionsofIntegrability

1.4LinearRecursiveFormulasfortheComputationofSingularPointValues

1.5TheAlgebraicConstructionofSingularValues

1.6ElementaryInvariantsoftheCubicSystems

1.7SingularPointValuesoftheQuadraticSystemsandtheHomogeneousCubicSystems

Chapter2TheoryofCenter-focusforaClassofInfiniteSingularPointsandHigher-orderSingularPoints

2.1ConversionoftheQuestions

2.2TheoryofCenter-focusattheInfinityforaClassofSystems

2.3TheoryofCenter-focusofHigher-orderSingularPointsforaClassofSystems

2.4TheConstructionofSingularPointValuesofHigher-orderSingularPointsandInfinity

2.5TranslationalInvarianceoftheSingularValuesatInfinity

Chapter3MultipleHopfBifurcations

3.1TheZerosofSuccessorFunctionsinthePolarCoordinates

3.2AnalyticEquivalence

3.3WeakBifurcationFunction

Chapter4BifurcationofLimitCyclesCreatedfromInfinityofSomePolynomialVectorFields

4.1CubicSystemsCreatedFourLimitCyclesatInfinity

4.2CubicSystemsCreatedSevenLimitCyclesatInfinity

Chapter5LocalandNon-localBifurcationsofPerturbedZq-equivatiantHamiltonianVectorFields

5.1Zq-equivariantPlanarVectorFieldsandanExample

5.2TheMethodofDetectionFunctions:RoughPerturbationsofZp-equivariantHamiltonianVectorFields

5.3BifurcationsofLimitCyclesofaZ2-equivariantPerturbedHamiltonianVectorFields

5.4TheRateofGrowthofHilbertNumberH(n)withn

Chapter6IsochronousCenter

6.1IsochronousCentersandPeriodConstants

6.2ComplexPeriodConstants

6.3ApplicationoftheMethodofSection6.2

6.4TheMethodofTime-angleDifference

6.5ConditionsofIsochronousCenterforaCubicSystem

6.6IsochronousCentersatInfinityofPolynomialSystems

Chapter7OnQuasiAnalyticSystems

7.1Preliminary

7.2ReductionoftheProblems

7.3FocalValues,PeriodicConstantsandFirstIntegralsof(7.2.3)

7.4SingularPointValuesandBifurcationsofLimitCyclesofQuasi-quadraticSystems

7.5IntegrabilityofQuasi-quadraticSystems

7.6NodePointValues

7.7IsochronousCenterofQuasi-quadraticSystems

Chapter8CompleteStudyonaBi-centerProblemfortheZ2-equivariantCubicVectorFields

8.1IntroductionandMainResults

8.2TheReductionofSystemHavingTwoElementaryFocusesat(1,0)and(-1,0)

8.3LyapunovConstants.InvariantIntegralsandtheNecessaryandSufficientConditionsoftheExistencefortheBi-center

8.4TheConditionsofSix-orderFineFocusof(8.3.2)andBifurcationsofLimitCycles

Bibliography

　　近年来，非线性动力学理论和方法正从低维向高维乃至无穷维发展。伴随着计算机代数、数值模拟和图形技术的进步，非线性动力学所处理的问题规模和难度不断提高。本套丛书更加侧重于对工程科学，生命科学，社会科学等领域中的非先行动力学问题进行建模，理论分析，计算和实验。与国外的同类丛书相比，它更具有整体的出版思想，每分册阐述一个主题，互不重复等特点。本书的选题为“二阶非线性系统的奇点量中心问题与极限环分叉”，该书为英文版。