李群在微分方程中的应用

图书标准信息

• 作者 P.J.Olver 编
• 出版社 世界图书出版公司
• 出版时间 1999-11
• 版次 2
• ISBN 9787506207300
• 定价 89.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 513页

【内容简介】

Thisbookisdevotedtoexplainingawiderangeofapplicationsofcontinuoussymmetrygroupstophysicallyimportantsystemsofdifferentialequations.Emphasisisplacedonsignificantapplicationsofgroup-theoreticmethods,organizedsothattheappliedreadercanreadilylearnthebasiccomputationaltechniquesrequiredforgenuinephysicalproblems.

【目录】

PrefacetoFirstEdition
PrefacetoSecondEdition
Acknowledgments
Introduction
NotestotheReader
CHAPTER1IntroductiontoLieGroups
1.1Manifolds
ChangeofCoordinates
MapsBetweenManifolds
TheMaximalRankCondition
Submanifolds
ReaularSubmanifolds
ImplicitSubmanifolds
CurvesandConnectedness
1.2LieGroups
LieSubgroups
LocalLieGroups
LocalTransformationGroups
Orbits
1.3.VectorFields
Flows
ActiononFunctions
Differentials
LieBrackets
TangentSpacesandVectorsFieldsonSubmanifolds
Frobenius'Theorem
1.4LieAlgebras
One-ParameterSubgroups
Subalgebras
TheExponentialMap
LieAlgebrasofLocalLieGroups
StructureConstants
CommutatorTables
InfinitesimalGroupActions
1.5.DifferentialForms
PuIl-BackandChangeofCoordinates
InteriorProducts
TheDifferential
ThedeRhamComplex
LieDerivatives
HomotopyOperators
IntegrationandStokes'Theorem
Notes
Exercises

CHAPTER2SymmetryGroupsofDifTerentialEquations
2.1SymmetriesofAlgebraicEquations
InvariantSubsets
InvariantFunctions
InfinitesimalInvariance
LocalInvariance
InvariantsandFunctionalDependence
MethodsforConstructingInvariants
2.2.GroupsandDifferentialEquations
2.3.Prolongation
SystemsofDifTerentialEquations
ProlongationofGroupActions
InvarianceofDifferentialEquations
ProlongationofVectorFields
InfinitesimalInvariance
TheProlongationFormula
TotalDerivatives
TheGeneralProlongationFormula
PropertiesofProlongedVectorFields
CharacteristicsofSymmetries
2.4.CalculationofSymmetryGroups
2.5.IntegrationofOrdinaryDifferentialEquations
FirstOrderEquations
HigherOrderEquations
DifferentialInvariants
Multi-parameterSymmetryGroups
SolvableGroups
SystemsofOrdinaryDifferentialEquations
2.6.NondegeneracyConditionsforDifferentialEquations
LocalSolvability
InvarianceCriteria
TheCauchy-KovalevskayaTheorem
Characteristics
NormalSystems
ProlongationofDifTerentialEquations
Notes
Exercises
CHAPTER3Group-InvariantSolutions
……
CHAPTER4SymmetryGroupsandConservationLaws
CHAPTER5GeneralizedSymmetries
CHAPTER6Finite-DimensionalHamiltonianSystems
CHAPTER7HamiltonianMethodsforEvolutionEquations
References
SymbolIndex
AuthorIndex
SubjectIndex