程崇庆南京大学长江特聘教授(基础数学)
南京大学副校长兼研究生院院长

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研究兴趣Hamilton动力系统：动力学不稳定性，连接轨道的变分构造，Arnold扩散，KAM理论与弱KAM理论数学论文•ChengC.Q.,VariationalconstructionofdiffusionorbitsforpositivedefiniteLagrangians,ProceedingsofIntnationalCongressofMathematiciansvol3(2010)1714-1728.
•ChengC.Q.&LiX.,VariationalconstructionofunboundedorbitsinLagrangiansystems,ScienceChina:Mathematics53(3)(2010)617-624.
•LiX.&ChengC.Q.,ConnectingorbitsofautonomousLagrangiansystems,Nonlinearity23(2010)119-141.
•ChengC.Q.&YanJ.,ArnolddiffusioninHamiltonianSystems:aprioriunstablecase,J.DifferentialGeometry,82(2009)229-277.
•ChengC.Q.&YanJ.,VariationalconstructionofdiffusionorbitsinconvexHamiltoniansystemswithmultipledegreesoffreedom,ProceedingsICCM’2004,AMS/IPStudiesinAdvancedMathematics42(2008)11-27.
•ChengC.Q.,VariationalmethodsfortheproblemofArnolddiffusion,inHamiltonianDynamicalsystemsandapplicationsWCraig(ed.)Springer(2008)337-366.
•ChengC.Q.,Hamiltoniansystems:stableorunstable?MilanJ.Math.74(2006)295-312.
•ZhengY.&ChengC.Q.,HomoclinicorbitsofpositivedefiniteLagrangiansystems,J.DifferentialEquations,229(2006)297-316.
•ChengC.Q.,MinimalinvarianttoriintheresonantregionsofnearlyintegrableHamiltoniansystems,TransactionsofAmericanMathematicalSociety357（12）(2005)5067-5095.
•CuiX.J.,ChengC.Q.&ChengW.,ExistenceofinfinitelymanyhomoclinicorbitstoAubrysetsforpositivedefiniteLagrangiansystems,J.DifferentialEquations,214(2005)176-188.
•ChengC.Q.&YanJ.,ExistenceofdiffusionorbitsinaprioriunstableHamiltoniansystems,J.DifferentialGeometry,67(2004)457-517.
•ChengC.Q.,KAM理论与Arnold扩散：Hamilton系统的动力学稳定性问题；中国科学，34卷第3期（2004）257-267.
•YanJ.&ChengC.Q.,DynamicsaroundminimalhyperbolictorusinHamiltoniansystems，Int.J.Mod.Phys.(B)17(2003)3950-3963.
•ChengW.&ChengC.Q.,ConnectingorbitsamongDenjoyminimalsetsformonotonetwistmap.ScienceinChina46(2003)159-168.
•王乾，程崇庆：退化情形下高余维双曲不变环面的存在性，中国科学，32卷7期，（2002）640-649.
•ChengC.Q.,AKAMtheoryforresonanttoriandageneralizationofPoincareBirkhofffixedpointtheorem.AMS/IPStudiesinAdvancedMathematics20(2001)397-401.
•ChengC.Q.&ChengJ.,DynamicalstabilityofHamiltoniansystems,ProgressinNaturalScience10(2000)343-349.
•ChengW.&ChengC.Q.,Existenceofinfinitelymanynon-Birkhoffperiodicorbitsintwistmaps,ScienceinChina43(2000)810-817.
•ChengW.&ChengC.Q.,Ontheconnectingorbitsamonglocalminimizersformonotonetwistmap,ProgressinNonlinearAnalysis6WorldScientific(2000)58-80.
•ChengC.Q.,LowerdimensionalinvarianttoriintheregionsofinstabilityfornearlyintegrableHamiltoniansystems,Commun.Math.Phys.203(1999)385-419.
•ChengC.Q.&WangS.L.,ThesurvivingoflowerdimensionaltorifromresonancetorusofHamiltoniansystems,J.Diff.Eqns.155(1999)311-326.
•ChengC.Q.&XiaZ.,KAMtheorywithoutthetwistcondition,DynamicalSystems-TheMemorialVolumeofLiaoS.T.,WorldScientific(1999)16-22.
•WangS.L.&ChengC.Q.,LowerdimensionaltoriforgenericHamiltoniansystemsChineseScienceBulletin44(1999)1187-1191.
•QianS.&ChengC.Q.,Infinitelymanyellipticperiodicorbitsinhigherdimensionalsymplecticdiffeomorphisms,NortheasternMath.J.15(1999)495-502.
•QinY.&ChengC.Q.,Thenon-monotonetwistmapsandbasichyperbolicsets,ScienceinChina41(1998)1176-1183.
•WangS.L.&ChengC.Q.,BirkhofflowerdimensionaltoriinHamiltoniansystems,ChineseScienceBulletin42(1997)1866-1870.
•ChengC.Q.,Birkhoff-Kolmogorov-Arnold-MosertoriinconvexHamiltoniansystems,Commun.Math.Phys.177(1996)529-559.
•ChengC.Q.&KupperT.,Dynamicalbehavioroftwosolitonsolutionsexhibitedbyperturbedsine-Gordonequation,Math.Nachr.171(1995)53-77.
•ChengC.Q.&SunY.S.,ExistenceofKAMtoriindegenerateHamiltoniansystems,J.Diff.Eqns.114(1994)288-335.
•ChengC.Q.,BifurcationsofvectorfieldswithZ4symmetry,DynamicalsystemsandRelatedTopics,9(1992)61-64.
•ChengC.Q.,Metamorphosesofphaseportraitofvectorfieldsinthecaseofsymmetryoforder4,J.Diff.Eqns.95(1992)130-139.
•ChengC.Q.,Invarianttorusbifurcationseriesandevolutionofchaosexhibitedbyaforcednonlinearvibrationsystem,Int.J.NonlinearMech.26(1991)105-116.
•ChengC.Q.,Hopfbifurcationsinnon-autonomoussystemsatpointsofresonance,ScienceinChina33(1990)206-219.
•ChengC.Q.,&SunY.S.,Existenceofinvarianttoriinthreedimensionalmeasure-preservingmappings,CelestialMechanicsandDynamicalAstronomy45(1989/1990)275-292.
•ChengC.Q.,&SunY.S.,Existenceofperiodicallyinvariantcurvesinthreedimensionalmeasure-preservingmappings,CelestialMechanicsandDynamicalAstronomy45(1989/1990)293-303.
•ChengC.Q.,AHopf-Landaubifurcationseriesdiscoveredinanonlinearvibrationsystem,ChineseScienceBulletin34(1989)1169-1172.
•ChengC.Q.,Hopfbifurcationatresonanceinnon-autonomoussystems,Appl.Math.Mech.10(1989)443-453.
•ChengC.Q.,Hopf-Landaubifurcationintohigherdimensionaltori.Appl.Math.Mech.10(1989)553-562.
•ChengC.Q.,Hopf-Landaubifurcationintohigherdimensionaltori,Proc.Int.Conf.Bifu.Th.&Numer.Anal.(1988)134-144.
•ChengC.Q.,Ontheconvergenceofsubstructuresynthesis,Proc.Int.Conf.VibrationProblemsinEngineering(1986)245-251.
•ChengC.Q.,Onthedecouplingproblemofequationofmotioninthecaseofcomplexmode(inChinesewithEnglishsummery)J.NanjingInstituteofTech.(1983)No.498-105.
预印本
•ChengC.Q.,Non-existenceofKAMtorus
•ChengC.Q.,ChengC.Q.,AbundanceofArnoldduffusioninaprioristable
著作
•程崇庆，孙义燧：哈密顿系统的有序与无序运动，上海科教出版社(1996).
获得学术奖励
2001年国家自然科学二等奖(第一完成人)
2000年中国高校自然科学一等奖(第一完成人)
1998年首届Morningside数学奖（银奖）
1997年香港求是杰出青年学者奖（数学）
部分国际会议邀请报告
•45-minutesinvitedtalk,26-thInternationalCongressofMathematicians,2010Hyderbad,India
•30-minutesinvitedtalk,16-thInternationalCongressofMathematicalPhysics,August3-8,2009,Prague,Czech
•Onehourinvitedtalk,NewConnectionsbetweenDynamicalSystemsandHamiltonianPDEs,June1-6,2009,Maiori,Italy
•Onehourinvitedtalk,ConferenceonweakKAMtheory,February1-6,2009,Nice,France
•Onehourinvitedtalk,ConferenceonStabilityandInstabilityinMechanicalSystems,September22-26,2008,Barcelona,Spain
•Mini-course,AdvancedCourseonStabilityandInstabilityinMechanicalSystems,September15-19,2008,Barcelona,Spain
•Mini-course,Hamiltoniandynamicalsystemsandapplications,June18-29,2007,Montreal,Canada
•One-hourinvitedtalk,ConferenceonDynamicalsystems,July10-16,2005,Oberwolfach,Germany
•50minutesinvitedtalk,InternationalConferenceonChaosandDynamicalComplexity,May16-20,2005,Hsinchu,Taiwan
•One-hourplenarylecture,The3rdInternationalCongressofChineseMathematicians,December17-24,2004，HongKong
•One-hourinvitedtalk,DynamicalDay,UniversityofParis7,December3,2004,Paris,France
•One-hourinvitedtalk,WorkshoponHamiltonianDynamicalSystems,May24-28,2004,Montreal,Canada
•One-hourinvitedtalk,ConferenceonDynamicalSystems,July15-21,2001,Oberwolfach,Germany
•One-hourinvitedtalk,ClayMathematicsInstituteSymposiumandEuro-WorkshoponHamiltonianSystems,May21-June1,2001,Edinburgh,UK
•45-minuteinvitedtalk,The3rdAsianMathematicalConference,October23-27,2000,Diliman,Philippines
•One-hourinvitedtalk,WorkshoponthedeterminationofhomoclinictrajectoriesinHamiltoniansystemsandArnold’sdiffusion,September6-17,1999,IHES,Paris,France
•45-minuteinvitedtalk,The1stInternationalCongressofChineseMathematicians,December12-16,1998,Beijing

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