Name:

Jiangong You

Position:
Professor

 

 

   
   
   

Research interests:
Differential Equations, Dynamical Systems, Dynamics of Hamiltonian PDEs, Spectral Theory of Schrodinger Operators

Education and Working Experience:

1979.9--1983.7:Bachelor's Degree, Dept. of Math., Jiangsu Normal Univ.;
1983.9--1986.7:Master*s Degree,Dept. of Math., Nanjing Univ.;
1986.9--1989.7:Ph. D. Degree,Dept. of Math.,Peking Univ.;
1989.7--1991.7:Post-doctor,Nanjing Univ.;
1991.8--1992.2:Lecturer,Nanjing Univ.;
1992.2--1998.1:Associate Professor,Nanjing Univ.;
1994.2--1994.8:Visiting Scholar,Forschungsinstitut fur Mathematik der Eidgenos-sische Technische Hochschule Zurich;
1995.5--1997.6:Humboldt Research Fellow,Universitaet zu Koeln, Technische Universitaet M邦nchen;
1998.2--1998.8:Visiting Scholar,Terza Universit角 degli Studi di Roma;
1998.2--2016.9:Professor,Nanjing Univ.;
2016.9--present:Professor,Chern Inst. of Math., Nankai Univ.


Publications:

1. (with Wang, Jing) Boundedness of solutions for non-linear differential equations with Liouvillean frequency. J. Differential Equations 261(2016), no, 2, 1068 每 1098.
2. (with Zhou, Qi) Simple counter-examples to Kotani-Last conjecture via reducibility,International Mathematics Research Notices IMRN 2015ㄛno. 19, 9450-9455.
3. (Zhang, Shiwen and Zhou, Qi) Point spectrum for quasi-periodic long range operators, J. Spectr. Theory 4 (2014), no, 4, 769 每 781.
4. (with Zhou, Qi) Phase transition and semi-global reducibility. Comm. Math. Phys. 330 (2014),no. 3, 1095每1113.
5. (with Zhang, Shiwen) Holder continuity of the Lyapunov exponent for analytic quasiperiodic Schrodinger cocycle with weak Liouville frequency. Ergodic Theory Dynam. Systems 34 (2014), no. 4, 1395每1408.
6. (with Geng, Jiansheng and Zhao, Zhiyan) Localization in one-dimensional quasi-periodic nonlinear systems. Geom. Funct. Anal. 24 (2014), no. 1, 116每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每333, Springer Proc. Math. 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每2412.
9. (with Zhou, QiㄛEmbedding of analytic quasi-periodic cocycles into analytic quasi-periodic linear systems and its applications. Comm. Math. Phys. 323 (2013), no. 3, 975每1005.
10. (with Wu, Jian) Reducibility of slow quasi-periodic linear systems, Proc. Amer. Math. Soc. 141(2013), no. 9, 3147 每 3155.
11. (with X. Hou) Almost reducibility and non-perturbative reducibility of quasi-periodic linear systems. Invent. Math. 190 (2012), no. 1, 209每260.
12. (with J. Geng and X. Xu) An infinite dimensional KAM theorem and its application to the two dimensional cubic Schr?dinger equation. Adv. Math. 226 (2011), no. 6, 5361每5402.
13. (with J. Xu) Persistence of the non-twist torus in nearly integrable Hamiltonian systems. Proc. Amer. Math. Soc. 138 (2010), no. 7, 2385每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每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每866.
16. (with X. Hou) The rigidity of reducibility of cocycles on SO(N ,R). Nonlinearity 21 (2008), no. 10, 2317每2330.
17. (with J. Xu) Gevrey-smoothness of invariant tori for analytic nearly integrable Hamiltonian systems under R邦ssmann's non-degeneracy condition. J. Differential Equations 235 (2007), no. 2, 609每622.
18. (with J. Geng) KAM Tori for Higher Dimensional Beam Equation with Constant Potentials, Nonlinearity 19 (2006), no. 10, 2405每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每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 Equations in Higher Dimensional Space, Communications in Mathematical Physics, Vol.262(2), 2006, 343-372.
22. (with H. Broer and H. Hanssmann) Umbilical Torus 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.Math.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-resonance 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 K-C.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 Physics, 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 Physics, 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. Qiu) 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(IㄛII), Science in China, Vol.39(4), 372-394, 1996.
41. (with Y. Wang) Boundedness of solutions for time dependent polynomial potentials with C2 coefficients, Z. Angew. Math. Phys. , Vol. 47, 1996.
42. (with J. Xu) On reducibility of linear differential equations with almost periodic coefficients, Chinese Journal of Contemporary Mathematics, Vol.17 (1996), 375-386.
43. Quasiperiodic solutions for a class of quasiperiodic forced differential equations, J. Math. Anal. And Appl. Vol.192(3), 1995.
44. (with B. Liu) Stability of a parabolic fixed point 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 time map, Differential and Integral EquationsㄛVol. 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, Chinese 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.


Awards:

1.The National Science Fund for Distinguished Young Scholars, 1999
2.Excellent Young Scholar Award, Hong Kong QiuShi Science and Technology Foundation, 2001
3.Award for Science and Technology of Chinese University (first class), 2001
4.Cheung Kong Scholar Professor 2001
5.National Award in Natural Science of China (second class), 2002


Contact:
Office: Room 407, Shiingshen Building