国外数学名著系列（续一）（影印版）51：动力系统7（可积系统，不完整动力系统）

图书标准信息

• 作者 [俄罗斯]阿诺德（V.I.Arnold）、[俄罗斯]阿诺德（V.I.Arnold） 著
• 出版社 科学出版社
• 出版时间 2009-01
• 版次 1
• ISBN 9787030234940
• 定价 80.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 341页
• 字数 430千字
• 正文语种 英语

【内容简介】

　　Thisvolumecontainsfivesurveysondynamicalsystems.Thefirstonedealswithnonholonomicmechanicsandgivesanupdatedandsystematictreatmentofthegeometryofdistributionsandofvariationalproblemswithnonintegrableconstraints.Themodernlanguageofdifferentialgeometryusedthroughoutthesurveyallowsforaclearandunifiedexpositionoftheearlierworkonnonholonomicproblems.Thereisadetaileddiscussionofthedynamicalpropertiesofthenonholonomicgeodesicflowandofvariousrelatedconcepts,suchasnonholonomicexponentialmapping,nonholonomicsphere,etc.
　　OthersurveystreatvariousaspectsofintegrableHamiltoniansystems,withanemphasisonLie-algebraicconstructions.Amongthetopicscoveredare：thegeneralizedCalogero-MosersystemsbasedonrootsystemsofsimpleLiealgebras,ageneralr-matrixschemeforconstructingintegrablesystemsandLaxpairs,linkswithfinite-gapintegrationtheory,topologicalaspectsofintegrablesystems,integrabletops,etc.Oneofthesurveysgivesathoroughanalysisofafamilyofquantumintegrablesystems(Todalattices)usingthemachineryofrepresentationtheory.
　　ReaderswillfindallthenewdifferentialgeometricandLiealgebraicmethodswhicharecurrentlyusedinthetheoryofintegrablesystemsinthisbook.Itwillbeindispensabletograduatestudentsandresearchersinmathematicsandtheoreticalphysics.

【目录】

Introduction
Chapter1.GeometryofDistributions
I.DistributionsandRelatedObjects
1.1.DistributionsandDifferentialSystems
1.2.FrobeniusTheoremandtheFlagofaDistribution
1.3.CodistributionsandPfaffianSystems
1.4.RegularDistributions
1.5.DistributionsInvariantwithRespecttoGroupActionsandSomeCanonicalExamples
1.6.ConnectionsasDistributions
1.7.AClassificationofLeftInvariantContactStructuresonThree-DimensionalLieGroups

2.GenericDistributionsandSetsofVectorFields，andDegeneraciesofSmallCodimension.NilpotentizationandClassificationProblem
2.1.GenericDistributions
2.2.NormalFormsofJetsofBasicVectorFieldsofaGenericDistribution
2.3.DegeneraciesofSmallCodimension
2.4.GenericSetsofVectorFields
2.5.SmallCodimensionDegeneraciesofSetsofVectorFields
2.6.ProjectionMapAssociatedwithaDistribution
2.7.ClassificatonofRegularDistributions
2.8.NilpotentizationandNilpotentCalculus

Chapter2.BasicTheoryofNonholonomicRiemannianManifolds
1.GeneralNonholonomicVariationalProblemandtheGeodesic
FlowonNonholonomicRiemannianManifolds
1.1.Rashevsky-ChowTheoremandNonholonomicRiemannianMetrics(Carnot-CaratheodoryMetrics)
1.2.Two-PointProblemandtheHopf-RinowTheorem
1.3.TheCauchyProblemandtheNonholonomicGeodesicFlow
1.4.TheEuler-LagrangeEquationsinInvariantFormandintheOrthogonalMovingFrameandNonholonomicGeodesics
1.5.TheStandardFormofEquationsofNonholonomicGeodesicsforGenericDistributions
1.6.NonholonomicExponentialMappingandtheWaveFront
1.7.TheActionFunctional

2.EstimatesoftheAccessibilitySet
2.1.TheParallelotopeTheorem
2.2.PolysystemsandFinslerianMetrics
2.3.TheoremontheLeadingTerm
2.4.EstimatesofGenericNonholonomicMetricsonCompactManifolds
2.5.HausdorffDimensionofNonholonomicRiemannianManifold!
2.6.TheNonhoionomicBallintheHeisenbergGroupastheLimitofPowersofaRiemannianBall

Chapter3.NonhoionomicVariationalProblemsonThree-DimensionalLieGroups
1.TheNonholonomice-SphereandtheWaveFront
1.1.ReductionoftheNonhoionomicGeodesicFlow
1.2.MetricTensorsonThree-DimensionalNonholonomicLieAlgebras
1.3.StructureConstantsofThree-DimensionalNonholonomicLieAlgebras
1.4.NormalFormsofEquationsofNonholonomicGeodesicsonThree-DimensionalLieGroups
1.5.TheFlowontheBaseV+VloftheSemidirectProduct
1.6.WaveFrontofNonholonomicGeodesicFlow，Nonholonomice-SphereandtheirSingularities
1.7.MetricStructureoftheSphere

2.NonholonomicGeodesicFlowonThree-DimensionalLieGroups
2.1.TheMonodromyMaps
2.2.NonholonomicGeodesicFlowonSO(3)
2.3.NG-FiowonCOmpactHomogeneousSpacesoftheHeisenbergGroup
2.4.NonholonomicGeodesicFlowsonCompactHomogeneousSpacesofSL
2.5.NonholonomicGeodesicFlowonSomeSpecialMultidimensionalNilmanifolds
References
AdditionalBibliographicalNotes