尤建功
南开大学教授、博士生导师
尤建功 ﹐男﹐1963年3月出生﹐江苏六合人,毕业于江苏师范大学
人物经历
现任南开大学陈省身数学研究所教授、博士生导师。1983年毕业于徐州师范学院﹔1989年获北京大学理学博士学位,1989-1991年在南京大学博士后,1986年获南京大学理学硕士学位﹔1989年获北京大学理学博士学位后到南京大学任教,任数学系系主任。1994年2月8日访问瑞士苏黎世高工(苏黎世联邦理工学院)数学研究所﹔1995年至1997年受德国洪堡基金会资助在科隆大学慕尼黑工业大学做合作研究﹔1998年2月至8月在罗马第三大学做访问教授。1998年成为国家非线性科学攀登项目组正式成员﹔1999年获得国家杰出青年基金﹔2000年成为国家重点基础研究发展规划项目组(非线性科学)成员。
1991年起历任南京大学讲师、副教授、教授、博士生导师、长江学者、数学系主任,2016年起任南开大学陈省身数学研究所教授、博士生导师。曾在德国科隆大学和慕尼黑工大做亚历山大·冯·洪堡学者;曾访问瑞士苏黎世高工(苏黎世联邦理工学院)数学研究所等多所国外著名大学。在Duffing方程的稳定性,KAM理论,哈密顿偏微分方程的拟周期运动、埃尔温·薛定谔映射的谱理论等方面做出了一系列深刻的工作。
2018年8月1日至8月9日,第28届国际数学家大会在巴西里约热内卢召开,尤建功教授应邀参加第28届国际数学家大会并于2日作45分钟特邀报告,报告题目为“定量几乎可约性理论及其应用”,主要介绍尤建功教授与合作者在拟周期线性系统可约性及其在算子谱理论中的应用方面的一些成果。这是自2002年以来,继龙以明院士、张伟平院士之后,南开大学学者又一次应邀在国际数学家大会上作主题报告。
国际数学家大会(International Congress of Mathematicians,简称ICM)是由国际数学联盟主办的全球性数学学术会议,是国际数学届的盛会,每四年举办一次。会议的主要内容是进行学术交流,并在开幕式上颁发菲尔兹奖(1936年起)、内万林纳奖(1982年起)、高斯奖(2006年起)和陈省身奖(2010年起)。首届国际数学家大会于1897年在瑞士苏黎世举行,至今共举办了27届。1900年巴黎大会之后,除两次世界大战期间外,国际数学家大会从未中断,2002年在中国北京举办了第24届大会。
在每届数学家大会上,组委会都会邀请一批在相关领域做出杰出工作的著名数学家作主题报告,这标志着数学家的工作得到了国际数学界的普遍认可和赞誉,同时,对于数学家而言,也是非常高的荣誉。
2021年8月,入选2021年中国科学院院士增选初步候选人名单。
任免信息
2017年12月,当选中国民主同盟第十二届中央委员会委员。
主要成就
研究方向
主要是动力系统﹐特别是Hamilton动力系统。
主要贡献
现承担国家基金委重点项目和国家重大基础研究规划项目。
研究成果主要集中在KAM理论及其在常微分方程偏微分方程中的应用方面﹔对低维环面的KAM理论做出了重要发展﹐在第一Melnikov非共振条件下得到了不变环面的存在性﹐并用于研究了国际上非常活跃的Hamilton偏微分方程的拟周期解问题﹔研究成果否定了1994年菲尔兹奖获得者Bourgain认为KAM理论不能用于重法频率的看法﹔解决了KAM理论创始人之一Moser关於摆方程Lagrange稳定性的一个公开问题﹔受到了国际同行的重视和好评。
学术论文
1.Persistence of lower dimensional tori under the first Melnikov's non-共振 condition, to appear in Journal de Mathematiques Pures et Appliquees, 2001(with J.Xu).
3.KAM tori for 1D nonlinear wave equations with periodic boundary condition, Communications in Mathematical 物理学, Vol. 211(2), 497-525, 2000(with l, Chierchia).
Almost reducibility and non-perturbative reducibility of quasi-periodic linear systems. Invent. 数学 190 (2012), no. 1, 209–260. Article; E-Journal.
X. Hou and J. You
An infinite dimensional KAM theorem and its application to the two dimensional cubic Schrödinger 方程 Adv. Math. 226 (2011), no. 6, 5361–5402. Article; E-Journal.
J. Gen.G, X. Xu and J. You
Persistence of the non-twist 环面 in nearly integrable Hamiltonian systems. Proc. Amer. 数学 Soc. 138 (2010), no. 7, 2385–2395.Article; E-Journal.
J. Xu and J. You
Local rigidity of reducibility of analytic quasi-periodic cocycles on U(n). Discrete Contin. Dyn. Syst. 24 (2009), no. 2, 441–454.Article; E-Journal.
X. Hou and J. You
Corrigendum for the paper: "Two-dimensional invariant tori in the Neighborhood of an elliptic Equilibrium of Hamiltonian systems" in Acta Mathematica Sinica, English Series August 2009, 容积单位 25, Issue 8, pp 1363-1378 Article
H. Lu and J. You
Two-dimensional invariant tori in the Neighborhood of an elliptic Equilibrium of Hamiltonian systems. Acta Mathematica Sinica, English Series August 2009, 容积单位 25, Issue 8, pp 1363-1378. Article; E-Journal.
H. Lu and J. You
Full measure reducibility for generic one-parameter family of quasi-periodic linear systems. J. DynamDifferential Equations 20 (2008), no. 4, 八三夭866. Article; E-Journal.
H. He and J. You
The rigidity of reducibility of cocycles on SO(N ,R). Nonlinearity 21 (2008),no. 10, 2317–2330. Article; E-Journal.
X. Hou and J. You
Diophantine vectors in analytic submanifolds of Euclidean spaces. Sci. China Ser. A. 50 (2007), no. 9, 1334–1338. Article; E-Journal.
R. Cao and J. You
Corrigendum for the paper: "Invariant tori for nearly integrable Hamiltonian systems with degeneracy" [数学 Z. 226 (1997), no. 3, 375–387] by Xu, You, and Q. 裘姓. Math. Z. 257 (2007), no. 4, 939. Article; E-Journal.
J. Xu and J. You
Gevrey-smoothness of invariant tori for analytic nearly integrable Hamiltonian systems under Rüssmann's non-degeneracy condition. J. Differential Equations 235 (2007), no. 2, 609–622. Article; E-Journal.
J. Xu and J. You
KAM Tori for Higher Dimensional Beam 方程 with Constant Potentials, Nonlinearity 19 (2006), no. 10, 2405–2423. Article; E-Journal.
J. Gen.G and J. You
The Existence of Integrable Invariant Manifolds of Hamiltonian Partial Differential Equations, Discrete and Continuous Dynamical Systems 16 (2006, no. 1-227–234. Article; E-Journal.
R.Cao and J. You
An Improved Result for Positive Measure Reducibility of Quasi- periodic Linear Systems, Acta Mathematica Sinica (English series) 22 1), 2006, 77-86. Article; E-Journal.
H. He and J. You
A KAM Theorem for Partial Differential Equations in Higher Dimensional Space乐队, Communications in Mathematical 物理学, Vol.262(2, 2006, 343-372. Article; E-Journal.
J.Gen.G and J.You
Umbilical 环面 Bifurcations in Hamiltonian Systems, J. Differential Equations, Vol. 222(1), 2006, 233-262. Article; E-Journal.
H. Broer, H. Hanssmann and J. You
A simple proof of diffusion approximations for LBFS re-entrant lines, Oper. Res. Lett., 34(2006), no. 2, 199–204. Article; E-Journal.
J. Yang, J.G. Dai, J. You and H. Zhang
Quasi-Periodic Solutions for 1D Schrödinger Equations with Higher Order Nonlinearity, SIAM J. Mathematical Analysis, 36(2005), 1965-1990. Article; E-Journal.
Z. Liang and J. You
Bifurcations of Normally Parabolic Tori in Hamiltonian Systems, Nonlinearity, 18 (2005) 1735-1769. Article; E-Journal.
H. Broer, H. Hanssmann and J. You
A KAM Theorem for One Dimensional Schrödinger 方程 with Periodic Boundary Conditions, J. Differential Equations, 209, 2005, 1-56. Article; E-Journal.
J. Gen.G and J. You
KAM tori of Hamiltonian perturbations of 1D linear beam equations, J.数学Anal.Appl., 277, 2003, 104-121. Article; E-Journal.
J. Geng and J. You
A Symplectic Map and its Application to the Persistence of Lower Dimensional InvariantTori, Science in China, 45(5), 2002,598-603. Article; E-Journal.
教学成果
• Mathematical Analysis (Fall 2005-2008, undergraduate freshman courses).
• Geometrical Methods in the Theory of Ordinary Differential Equations (Fall 2009-2011, undergraduate junior courses).
• Seminar of Dynamical Systems (Spring 2011-2014, undergraduate junior courses).
• Dynamical Systems (Spring 2008-2010, graduate courses).
• Differential Dynamical Systems (Spring 2011, graduate course).
• Hamiltonian Systems and N-Body Problems(Spring 2012, graduate course).
• Chaos in Dynamical Systems (Spring 2013, graduate course).
研究成果
1.(with Wang, Jing) Boundedness of solutions for non-linear differential equations with Liouvillean 频率 J. Differential 方程s 261(2016), no, 2, 1068 – 1098.
2.(with Zhou, Qi) Simple counter-examples to Kotani-Last conjecture via reducibility,International 数学 Research Notices IMRN 2015,no. 19, 9450-9455. 
3.(Zhang, Shiwen and Zhou, Qi) 小数点 spectrum for quasi-periodic long range operators, J. Spectr. Theory 4 (2014), no, 4, 769 – 781. 
4.(with Zhou, Qi) Phase transition and semi-global reducibility. Comm. 数学 Phys. 330 (2014),no. 3, 1095–1113. 
5.(with Zhang, Shiwen) Holder continuity of the Lyapunov exponent for analytic quasiperiodic Schrodinger cocycle with weak Liouville 频率 Ergodic Theory Dynam. Systems 34 (2014), no. 4, 1395–1408.
6.(with Gen.G, Jiansheng and Zhao, Zhiyan) Localization in ONE FCdimensional quasi-periodic nonlinear systems. Geom. Funct. Anal. 24 (2014), no. 1, 116–158.
7.(with Broer, Henk W. and Hanbmann, Heinz) On the Destruction of resonant Lagrangean tori in Hamiltonian systems. Recent trends in dynamical systems, 317–333, Springer Proc. 数学 Stat., 35, Springer, Basel, 2013. 
8.(with Wang, Yiqian) Examples of discontinuity of Lyapunov exponent in smooth quasiperiodic cocycles. Duke Math. J. 162 (2013), no. 13, 2363–2412. 
9.(with Zhou, Qi,Embedding of analytic quasi-periodic cocycles into analytic quasi-periodic linear systems and its applications. Comm. 数学 Phys. 323 (2013), no. 3, 975–1005.
10.(with Wu, Jian) Reducibility of slow quasi-periodic linear systems, Proc. Amer. Math. Soc. 141(2013), no. 9, 3147 – 3155.
11.(with X. Hou) Almost reducibility and non-perturbative reducibility of quasi-periodic linear systems. Invent. 数学 190 (2012), no. 1, 209–260. 
12.(with J. Geng and X. Xu) An infinite dimensional KAM theorem and its application to the two dimensional cubic Schr?dinger 方程. Adv. Math. 226 (2011), no. 6, 5361–5402. 
13.(with J. Xu) Persistence of the non-twist 环面 in nearly integrable Hamiltonian systems. Proc. Amer. 数学 Soc. 138 (2010), no. 7, 2385–2395. 
14.(with X. Hou) Local rigidity of reducibility of analytic quasi-periodic cocycles on U(n). Discrete Contin. Dyn. Syst. 24 (2009), no. 2, 441–454. 
15.(with H. He) Full measure reducibility for generic one-parameter family of quasi-periodic linear systems. J. Dynam. Differential Equations 20 (2008), no. 4, 831–866. 
16.(with X. Hou) The rigidity of reducibility of cocycles on SO(N ,R). Nonlinearity 21 (2008), no. 10, 2317–2330. 
17.(with J. Xu) Gevrey-smoothness of invariant tori for analytic nearly integrable Hamiltonian systems under Rüssmann's non-degeneracy condition. J. Differential Equations 235 (2007), no. 2, 609–622. 
18.(with J. Geng) KAM Tori for Higher Dimensional Beam Equation with Constant Potentials, Nonlinearity 19 (2006), no. 10, 2405–2423. 
19.(with R.Cao) The Existence of Integrable Invariant Manifolds of Hamiltonian Partial Differential Equations, Discrete and Continuous Dynamical Systems 16 (2006), no. 1, 227–234. 
20.(with H. He) An Improved Result for Positive Measure Reducibility of Quasi- periodic Linear Systems, Acta Mathematica Sinica (English series) 22 (1), 2006, 77-86. 
21.(with J.Geng) A KAM Theorem for Partial Differential 方程s in Higher Dimensional Space, Communications in Mathematical 物理学, Vol.262(2), 2006, 343-372. 
22.(with H. Broer and H. Hanssmann) Umbilical 环面 Bifurcations in Hamiltonian Systems, J. Differential Equations, Vol. 222(1), 2006, 233-262. 
23.(with Z. Liang) Quasi-Periodic Solutions for 1D Schrodinger Equations with Higher Order Nonlinearity, SIAM J. Mathematical Analysis, 36(2005), 1965-1990. 
24.(with H. Broer and H. Hanssmann) Bifurcations of Normally Parabolic Tori in Hamiltonian Systems, Nonlinearity, 18 (2005) 1735-1769. 
25.(with J. Geng) A KAM Theorem for One Dimensional Schrodinger Equation with Periodic Boundary Conditions, J. Differential Equations, 209, 2005, 1-56. 
26.(with J. Geng) KAM tori of Hamiltonian perturbations of 1D linear beam equations, J.数学Anal.Appl., 277, 2003, 104-121. 
27.(with J. Xu) A Symplectic Map and its Application to the Persistence of Lower Dimensional InvariantTori, Science in China, 45(5), 2002, 598-603. 
28.(with J. Xu) Persistence of lower dimensional tori under the first Melnikov’s non-共振 condition, Journal de Mathematiques Pures et Appliquees, 80 (10), 2001, 1045-1067. 
29.KAM theory for lower dimensional tori of nearly integrable Hamiltonian systems, Progress in Nonlinear Analysis, edited by 圆锥角膜Chang and Y. Long, World Scientific, 2000, 409-423. 
30.(with L. Chierchia) KAM tori for 1D nonlinear wave equations with periodic boundary conditions, Communications in Mathematical 物理学, Vol.211(2, 497-525, 2000. 
31.(with F-Z. Cong, T. Kupper and Y. Li) KAM-type theorem on resonant surfaces for nearly integrable Hamiltonian systems, J. Nonlinear Science, Vol.10, 49-68, 2000. 
32.Lower dimensional tori of reversible Hamiltonian systems in the resonant zone, Dynamical Systems, Proceedings of the International Conference in Honor of Professor Liao Shantao, 9-12, August, 1998. Editors, Yunping Jiang, Lan Wen, World Scientific, 1999, 301-314. 
33.Perturbations of lower dimensional tori for Hamiltonian systems, J.Differential Equations, Vol. 152, 1-29, 1999.
34.(with T. Kupper) Existence of quasiperiodic solutions and Littlewood's boundedness problem of Duffing equations with subquadratic potentials, Nonlinear Anal. 35 (1999), no. 5, Ser. A: Theory Methods, 549-559. 
35.A KAM theorem for hyperbolic type degenerate lower dimensional tori in Hamiltonian systems, Communications in Mathematical 物理学, Vol.192, 145-168, 1998. 
36.(with B. Liu) Quasiperiodic solutions of Duffing's Equations, J. Nonlinear Analysis: TMA, 1998.
37.(with M. Levi) Oscillatory escape in a Duffing equation with Polynomial potentials, J. Differential Equations, Vol.140, pp 415-426, 1997. 
38.(with M. Kunze and T. Kupper) On the Application of KAM Theory to Discontinuous Dynamical Systems, J. Differential Equations, Vol. 139, pp.1-21, 1997. 
39.(with J. Xu and Q. 裘姓) Invariant tori of nearly integrable Hamiltonian systems with degeneracy, Mathematische Zeitschrift, Vol.226, 375-386, 1997.
40.(with J. Xu and Q. Qiu) A KAM Theorem of Degenerate Infinite Dimensional Hamiltonian Systems(I,II), Science in China, Vol.39(4), 372-394, 1996. 
41.(with Y. Wang) Boundedness of solutions for 时间 dependent 多项式 potentials with C2 coefficients, Z. Angew. 数学 Phys. , Vol. 47, 1996. 
42.(with J. Xu) On reducibility of linear differential equations with almost periodic coefficients, 汉语词类 Journal of CONTEMPORARY Mathematics, Vol.17 (1996), 375-386. 
43.Quasiperiodic solutions for a class of quasiperiodic forced differential equations, J. 数学 Anal. And Appl. Vol.192(3), 1995. 
44.(with B. Liu) Stability of a parabolic fixed 小数点 of reversible mappings, Chin. Ann. of Math. (Series B), Vol. 15(2), 1994, 147-152. 
45.(with D. Qian) Periodic solutions of forced second order equations with the oscillatory 时间 map, Differential and Integral Equations,Vol. 6(4) 793-806, 1993.
46.Boundedness for solutions of superlinear Duffing's equations via the twist theorem, Science in China (series A), 35(4), 1992, 399-412.
47.Boundenness of solutions and quasiperiodic solutions of nonconservative Pendulum systems in a certain class, 汉语词类 Bulletin of Science (Kexue Tongbao), 36(21), 1991, 1906-1909. 
48.Invariant tori and Lagrange stability of pendulum type equations, J. Differential Equations, 85(1), 1990, 54-65.。
获得荣誉
曾获得国家杰出青年基金、香港求是科技基金会杰出青年学者奖、中国高校科技进步奖一等(排名第二)、第六届江苏省青年科技奖、国家自然科学二等奖(排名第三)。
2022年11月19日消息,南开大学陈省身数学研究所教授尤建功因其对动力系统的重要贡献,获得2024年度发展中国家科学院院士(英文简称TWAS)数学奖
2023年8月31日,入选2023年中国科学院院士增选有效候选人名单。
参考资料
中国民主同盟第十二届中央委员会.中国民主同盟.2017-12-22
尤建功.南开大学陈省身数学研究所.2021-12-08
目录
概述
人物经历
任免信息
主要成就
研究方向
主要贡献
学术论文
教学成果
研究成果
获得荣誉
参考资料