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P.J.Olver 编 / 世界图书出版公司 / 1999-11 / 平装
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李群在微分方程中的应用
Thisbookisdevotedtoexplainingawiderangeofapplicationsofcontinuoussymmetrygroupstophysicallyimportantsystemsofdifferentialequations.Emphasisisplacedonsignificantapplicationsofgroup-theoreticmethods,organizedsothattheappliedreadercanreadilylearnthebasiccomputationaltechniquesrequiredforgenuinephysicalproblems.
PrefacetoFirstEditionPrefacetoSecondEditionAcknowledgmentsIntroductionNotestotheReaderCHAPTER1IntroductiontoLieGroups1.1ManifoldsChangeofCoordinatesMapsBetweenManifoldsTheMaximalRankConditionSubmanifoldsReaularSubmanifoldsImplicitSubmanifoldsCurvesandConnectedness1.2LieGroupsLieSubgroupsLocalLieGroupsLocalTransformationGroupsOrbits1.3.VectorFieldsFlowsActiononFunctionsDifferentialsLieBracketsTangentSpacesandVectorsFieldsonSubmanifoldsFrobenius'Theorem1.4LieAlgebrasOne-ParameterSubgroupsSubalgebrasTheExponentialMapLieAlgebrasofLocalLieGroupsStructureConstantsCommutatorTablesInfinitesimalGroupActions1.5.DifferentialFormsPuIl-BackandChangeofCoordinatesInteriorProductsTheDifferentialThedeRhamComplexLieDerivativesHomotopyOperatorsIntegrationandStokes'TheoremNotesExercisesCHAPTER2SymmetryGroupsofDifTerentialEquations2.1SymmetriesofAlgebraicEquationsInvariantSubsetsInvariantFunctionsInfinitesimalInvarianceLocalInvarianceInvariantsandFunctionalDependenceMethodsforConstructingInvariants2.2.GroupsandDifferentialEquations2.3.ProlongationSystemsofDifTerentialEquationsProlongationofGroupActionsInvarianceofDifferentialEquationsProlongationofVectorFieldsInfinitesimalInvarianceTheProlongationFormulaTotalDerivativesTheGeneralProlongationFormulaPropertiesofProlongedVectorFieldsCharacteristicsofSymmetries2.4.CalculationofSymmetryGroups2.5.IntegrationofOrdinaryDifferentialEquationsFirstOrderEquationsHigherOrderEquationsDifferentialInvariantsMulti-parameterSymmetryGroupsSolvableGroupsSystemsofOrdinaryDifferentialEquations2.6.NondegeneracyConditionsforDifferentialEquationsLocalSolvabilityInvarianceCriteriaTheCauchy-KovalevskayaTheoremCharacteristicsNormalSystemsProlongationofDifTerentialEquationsNotesExercisesCHAPTER3Group-InvariantSolutions……CHAPTER4SymmetryGroupsandConservationLawsCHAPTER5GeneralizedSymmetriesCHAPTER6Finite-DimensionalHamiltonianSystemsCHAPTER7HamiltonianMethodsforEvolutionEquationsReferencesSymbolIndexAuthorIndexSubjectIndex
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