动力系统．7，可积系统，不完整动力系统

Ⅰ.NonholonomicDynamicalSystems,GeometryofDistributionsandVariationalProblems

Ⅱ.IntegrableSystemsⅡ

Chapter1IntegrableSystemsandFinite-DimensionalLieAlgebras

Chapter2Group-TheoreticalMethodsintheTheoryofFinite-DimensionalIntegrableSystems

Chapter3QuantizationofOpenTodaLattices

Ⅲ.GeometricandAlgebraicMechanismsoftheIntegrabilityofHamiltonianSystemsonHomogeneousSpacesandLieAlgebras

AuthorIndex

SubjectIndex

　　要使我国的数学事业更好地发展起来，需要数学家淡泊名利并付出更艰苦地努力。另一方面，我们也要从客观上为数学家创造更有利的发展数学事业的外部环境，这主要是加强对数学事业的支持与投资力度，使数学家有较好的工作与生活条件，其中也包括改善与加强数学的出版工作。这次科学出版社购买了版权，一次影印了23本施普林格出版社出版的数学书，就是一件好事，也是值得继续做下去的事情。大体上分一下，这23本书中，包括基础数学书5本，应用数学书6本与计算数学书12本，其中有些也具有交叉性质。这些书可以使读者较快地了解数学某方面的前沿，对从事这方面研究的数学家了解该领域的前沿与全貌也很有帮助。　　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.